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Probabilitate-banaketa Розподіл імовірностей Distribució de probabilitat Rozkład prawdopodobieństwa Distribución de probabilidad Kansverdeling Probability distribution Sannolikhetsfördelning Distribuição de probabilidade 확률 분포 確率分布 Probablodistribuo Распределение вероятностей Κατανομή πιθανότητας Wahrscheinlichkeitsverteilung Sebaran probabilitas 概率分布 Rozdělení pravděpodobnosti توزيع احتمال Loi de probabilité
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In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space). Em teoria da probabilidade e em estatística, uma distribuição de probabilidade descreve o comportamento aleatório de um fenômeno dependente do acaso. O estudo dos fenômenos aleatórios começou com o estudo dos jogos de azar – jogos de dados, sorteios de bolas de urna e cara ou coroa eram motivações para compreender e prever os experimentos aleatórios. Essas abordagens iniciais são fenômenos discretos, o que significa que o número de resultados possíveis é finito ou contável. Entretanto, certas questões revelam distribuições de probabilidade com suporte infinito não contável. Por exemplo, quando o lançamento de uma moeda tende ao infinito, o número de coroas aproxima-se de uma distribuição normal. Dalam teori peluang dan statistika, sebaran probabilitas, distribusi probabilitas, atau sebaran peluang menunjukkan besarnya probabilitas dari setiap (outcome) yang muncul dalam suatu acak (random). Berdasarkan pembentukannya, sebaran probabilitas dapat bersifat empirik atau bersifat teoretik. Sebaran empirik terbentuk dari hasil sensus atau mengambilan /contoh. Besar peluang yang terbentuk untuk setiap hasil tidak dapat diprediksi dan harus diturunkan dari hasil pengamatan. Teori statistika, tetapi demikian, lebih menyukai sebaran teoretik karena besar peluang dapat dihitung melalui fungsi yang sudah tertentu. En probabilitats i estadística les expressions distribució de probabilitat o llei de probabilitat tenen diversos sentits: per nombrosos autors, són sinònimes de Probabilitat, però molts altres autors les reserven per a les probabilitats a , . Però hi ha unanimitat en els termes llei o distribució d'una variable aleatòria o vector aleatori per referir-se a la probabilitat sobre induïda per la variable aleatòria o vector aleatori. Atès que hi ha una correspondència bijectiva entre les probabilitats sobre i les funcions de distribució, es pot donar la distribució d'una variable aleatòria o vector mitjançant la seva funció de distribució; si bé això és interessant des del punt dels resultats generals, per a distribucions de variables o vectors concrets (normals, binomials, etc) les funcions d 確率分布(かくりつぶんぷ、英: probability distribution)は、確率変数に対して、各々の値をとる確率全体を表したものである。日本産業規格では、「確率変数がある値となる確率,又はある集合に属する確率を与える関数」と定義している。 Sannolikhetsfördelning är inom sannolikhetsteori, statistik och matematisk statistik, en beskrivning (ofta i form av en funktion) av sannolikheterna för utfallen i ett utfallsrum. Sannolikhetsfördelningar, ibland bara "fördelningar", förekommer i både diskreta och kontinuerliga utfallsrum och kallas därför ibland diskret fördelning eller kontinuerlig fördelning, för att ange typen av utfallsrum. Στις Πιθανότητες και στην Στατιστική, η κατανομή πιθανοτήτων αποδίδει την πιθανότητα σε κάθε μετρήσιμο υποσύνολο των πιθανών αποτελεσμάτων του τυχαίου πειράματος,της έρευνας, ή την διαδικασία της επαγωγικής στατιστικής. Παραδείγματα αποτελούν τα πειράματα των οποίων ο δειγματικός χώρος είναι μη-αριθμητικός, όπου η κατανομή θα είναι μια κατηγορική κατανομή. Πειράματα των οποίων ο δειγματικός χώρος αποτελείται από διακριτές τυχαίες μεταβλητές, όπου η κατανομή μπορεί να καθορίζεται από μια συνάρτηση συσσωρευμένης πιθανότητας.Τα πειράματα με δειγματικούς χώρους κωδικοποιούνται από συνεχείς τυχαίες μεταβλητές, όπου η κατανομή μπορεί να καθορίζεται από μια συνάρτηση πυκνότητας πιθανότητας. Πιο πολύπλοκα πειράματα, όπως εκείνα που αφορούν στοχαστικές διαδικασίες που ορίζονται σε συνεχή χρόνο, μπο في علم الاحتمالات والإحصائيات، توزيع الاحتمال (بالإنجليزية: Probability distribution)‏ هو إعطاء احتمال معين لكل مجموعة جزئية قابلة للقياس من مجموعة نتائج تجربة عشوائية ما. وبتعبير آخر، هو قياس احتمالي مجاله تطبيق على مجموعة الأعداد الحقيقية. التوزيع الاحتمالي يعتبر حالة خاصة من مصطلح أكثر عمومية هو ، الذي يعتبر دالة تربط قيم احتمالات بمجموعات مقيسة من بحيث تحقق . كل متغير عشوائي ينشأعنه توزيع احتمالي يحتوي معظم المعلومات المهمة عن هذا المتغير. فاذا كان المتغير X متغيرا عشوائيا فان التوزيع الاحتمالي الموافق له ينسب للمجال [a, b] احتمالا : بمعنى أن احتمال أن يأخذ المتغير قيمة ضمن المجال هي : . 機率分布(英語:probability distribution)簡稱分布,亦稱機率分配或分配,是概率論中的一個概念。 使用時可以有以下兩種含義: * 廣義地,它指稱:隨機變量的概率性質——當我們說概率空間中的兩個隨機變量X和Y具有同樣的分布時,我們是無法用概率來區別他們的。換言之: 稱X和Y為同分布的隨機變量,當且僅當對任意事件,有成立。 但是,不能認為同分布的隨機變量是相同的隨機變量。事實上即使X與Y同分布,也可以没有任何點ω使得X(ω)=Y(ω)。在這個意義下,可以把隨機變量分類,每一類稱作一個分布,其中的所有隨機變量都同分布。用更簡要的語言來說,同分布是一種等價關係,每一個等價類就是一個分布。需注意的是,通常談到的離散分布、均勻分布、伯努利分布、正態分布、泊松分布等,都是指各種類型的分布,而不能視作一個分布。 * 狹義地,它是指:隨機變量的概率分布函數。設X是樣本空間上的隨機變量,為概率測度,則稱如下定義的函數是X的分布函數,或稱累積分布函數: ,對任意實數定義。 具有相同分布函數的隨機變量一定是同分布的,因此可以用分布函數來描述一個分布,但更常用的描述手段是概率密度函數。 En matematiko kaj statistiko, probablodistribuo aŭ probablodenso estas asigno de probablo al ĉiu intervalo de la reelaj nombroj, tiel ke la estas kontentigita. En teknika terminoj, probablodistribuo estas probablo kies domajno estas la sur la reelaj nombroj. La probablodistribuo indikas, kiel la probableco dividiĝas inter la eblaj hazardaj rezultoj, aparte la eblaj rezultoj de hazarda variablo.La statistiko kvante mezuras la hazardon kaj estas la teoria kontraŭparto de la empiria oftecodistribuo, kiu rezultiĝas el analizo de reale havigitaj mezuraj rezultoj. Rozkład prawdopodobieństwa – miara probabilistyczna określona na zbiorze wartości pewnej zmiennej losowej (wektora losowego), przypisująca prawdopodobieństwa wartościom tej zmiennej. Formalnie rozkład prawdopodobieństwa można rozpatrywać bez odwołania się do zmiennych losowych. У математиці та статистиці розпо́діл імові́рностей (який має математично описуватися функцією розподілу ймовірностей), ставить у відповідність кожному інтервалу ймовірність таким чином, що аксіоми ймовірностей виконуються. Математичною мовою, функція розподілу ймовірностей є ймовірнісною мірою, визначеною на борелівській алгебрі інтервалів. Розподіл імовірностей є окремим випадком загальнішого означення ймовірнісної міри, яка є функцією, що ставить у відповідність вимірним множинам з вимірного простору ймовірності за аксіомами Колмогорова. Probabilitate teorian eta estatistikan, probabilitate-banaketa batek zorizko aldagai batek har ditzakeen balioak, balio hauei dagokien probabilitateekin batera, ezartzen ditu. Probabilitate banaketa diskretuak eta jarraiak izan daitezke. Diskretua edo jarraitua den, probabilitate banaketa era ezberdinetan definitzen da. En teoría de la probabilidad y estadística, la distribución de probabilidad de una variable aleatoria es una función que asigna a cada suceso definido sobre la variable, la probabilidad de que dicho suceso ocurra. La distribución de probabilidad está definida sobre el conjunto de todos los sucesos y cada uno de los sucesos es el rango de valores de la variable aleatoria. También puede decirse que tiene una relación estrecha con las distribuciones de frecuencia. De hecho, una distribución de probabilidades puede comprenderse como una frecuencia teórica, ya que describe cómo se espera que varíen los resultados. 확률 분포(確率 分布, probability distribution)는 확률 변수가 특정한 값을 가질 확률을 나타내는 함수를 의미한다. 예를 들어, 주사위를 던졌을 때 나오는 눈에 대한 확률변수가 있을 때, 그 변수의 확률분포는 이산균등분포가 된다. 확률 분포는 확률 변수가 어떤 종류의 값을 가지는가에 따라서 크게 와 중 하나에 속하며, 둘 중 어디에도 속하지 않는 경우도 존재한다. Rozdělení pravděpodobnosti nebo rozložení pravděpodobnosti (někdy také distribuce pravděpodobnosti) náhodné veličiny je pravidlo, kterým se každému jevu popisovanému touto veličinou přiřazuje určitá pravděpodobnost. Rozdělení pravděpodobnosti náhodné veličiny vznikne, pokud je každé hodnotě diskrétní náhodné veličiny nebo intervalu hodnot spojité náhodné veličiny přiřazena pravděpodobnost. Rozdělení pravděpodobnosti lze také chápat jako zobrazení, které každému elementárnímu jevu přiřazuje určité reálné číslo, které charakterizuje pravděpodobnost tohoto jevu. Распределение вероятностей — это закон, описывающий область значений случайной величины и соответствующие вероятности появления этих значений. En théorie des probabilités et en statistique, une loi de probabilité décrit le comportement aléatoire d'un phénomène dépendant du hasard. L'étude des phénomènes aléatoires a commencé avec l'étude des jeux de hasard. Jeux de dés, tirage de boules dans des urnes et jeu de pile ou face ont été des motivations pour comprendre et prévoir les expériences aléatoires. Ces premières approches sont des phénomènes discrets, c'est-à-dire dont le nombre de résultats possibles est fini ou dénombrable. Certaines questions ont cependant fait apparaître des lois à support infini non dénombrable ; par exemple, lorsque le nombre de tirages de pile ou face effectués tend vers l'infini, la répartition des fréquences avec lesquelles le côté pile apparaît s'approche d'une loi normale. In de kansrekening speelt het begrip kansverdeling, waarschijnlijkheidsverdeling of -distributie (niet te verwarren met de distributie in de analyse) een centrale rol. Bij een experiment waarin het toeval een rol speelt, geeft de kansverdeling aan hoe "de kansen verdeeld zijn", d.w.z. wat de kans is op ieder van de verschillende, mogelijke uitkomsten. In de theorie wordt hier een specifieke betekenis aan gegeven: de 'kansverdeling' duidt op het geheel van mogelijke uitkomsten en de bijbehorende kansen.
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Probability distribution
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У математиці та статистиці розпо́діл імові́рностей (який має математично описуватися функцією розподілу ймовірностей), ставить у відповідність кожному інтервалу ймовірність таким чином, що аксіоми ймовірностей виконуються. Математичною мовою, функція розподілу ймовірностей є ймовірнісною мірою, визначеною на борелівській алгебрі інтервалів. Розподіл імовірностей є окремим випадком загальнішого означення ймовірнісної міри, яка є функцією, що ставить у відповідність вимірним множинам з вимірного простору ймовірності за аксіомами Колмогорова. Згідно з означенням П. Лапласа, мірою ймовірності є дріб, чисельником якого є число сприятливих подій, а знаменником — число всіх можливих випадків. Також деякі вчені означають розподіл як ймовірнісну міру, індуковану випадковою величиною X на деякому інтервалі — ймовірність множини B є . Однак у цій статті розглядаємо лише ймовірнісні міри на множині інтервалів числової прямої. Rozdělení pravděpodobnosti nebo rozložení pravděpodobnosti (někdy také distribuce pravděpodobnosti) náhodné veličiny je pravidlo, kterým se každému jevu popisovanému touto veličinou přiřazuje určitá pravděpodobnost. Rozdělení pravděpodobnosti náhodné veličiny vznikne, pokud je každé hodnotě diskrétní náhodné veličiny nebo intervalu hodnot spojité náhodné veličiny přiřazena pravděpodobnost. Rozdělení pravděpodobnosti lze také chápat jako zobrazení, které každému elementárnímu jevu přiřazuje určité reálné číslo, které charakterizuje pravděpodobnost tohoto jevu. Sannolikhetsfördelning är inom sannolikhetsteori, statistik och matematisk statistik, en beskrivning (ofta i form av en funktion) av sannolikheterna för utfallen i ett utfallsrum. Sannolikhetsfördelningar, ibland bara "fördelningar", förekommer i både diskreta och kontinuerliga utfallsrum och kallas därför ibland diskret fördelning eller kontinuerlig fördelning, för att ange typen av utfallsrum. Exempelvis är en likformig fördelning en fördelning där alla utfall är lika sannolika, vilket är fallet till exempel vid en dragning av ett nummer i en lottorad: där är alla utfall i det diskreta utfallsrummet [1, 2, 3, ... 34, 35] lika sannolika med sannolikheten 1/35. Распределение вероятностей — это закон, описывающий область значений случайной величины и соответствующие вероятности появления этих значений. Rozkład prawdopodobieństwa – miara probabilistyczna określona na zbiorze wartości pewnej zmiennej losowej (wektora losowego), przypisująca prawdopodobieństwa wartościom tej zmiennej. Formalnie rozkład prawdopodobieństwa można rozpatrywać bez odwołania się do zmiennych losowych. 機率分布(英語:probability distribution)簡稱分布,亦稱機率分配或分配,是概率論中的一個概念。 使用時可以有以下兩種含義: * 廣義地,它指稱:隨機變量的概率性質——當我們說概率空間中的兩個隨機變量X和Y具有同樣的分布時,我們是無法用概率來區別他們的。換言之: 稱X和Y為同分布的隨機變量,當且僅當對任意事件,有成立。 但是,不能認為同分布的隨機變量是相同的隨機變量。事實上即使X與Y同分布,也可以没有任何點ω使得X(ω)=Y(ω)。在這個意義下,可以把隨機變量分類,每一類稱作一個分布,其中的所有隨機變量都同分布。用更簡要的語言來說,同分布是一種等價關係,每一個等價類就是一個分布。需注意的是,通常談到的離散分布、均勻分布、伯努利分布、正態分布、泊松分布等,都是指各種類型的分布,而不能視作一個分布。 * 狹義地,它是指:隨機變量的概率分布函數。設X是樣本空間上的隨機變量,為概率測度,則稱如下定義的函數是X的分布函數,或稱累積分布函數: ,對任意實數定義。 具有相同分布函數的隨機變量一定是同分布的,因此可以用分布函數來描述一個分布,但更常用的描述手段是概率密度函數。 En probabilitats i estadística les expressions distribució de probabilitat o llei de probabilitat tenen diversos sentits: per nombrosos autors, són sinònimes de Probabilitat, però molts altres autors les reserven per a les probabilitats a , . Però hi ha unanimitat en els termes llei o distribució d'una variable aleatòria o vector aleatori per referir-se a la probabilitat sobre induïda per la variable aleatòria o vector aleatori. Atès que hi ha una correspondència bijectiva entre les probabilitats sobre i les funcions de distribució, es pot donar la distribució d'una variable aleatòria o vector mitjançant la seva funció de distribució; si bé això és interessant des del punt dels resultats generals, per a distribucions de variables o vectors concrets (normals, binomials, etc) les funcions de distribució són sovint feixugues d'utilitzar, i llavors és molt habitual fer servir la funció de densitat (cas absolutament continu), la funció de probabilitat (cas discret), la funció característica o alguna altra transformació que determini unívocament la distribució. Dalam teori peluang dan statistika, sebaran probabilitas, distribusi probabilitas, atau sebaran peluang menunjukkan besarnya probabilitas dari setiap (outcome) yang muncul dalam suatu acak (random). Berdasarkan pembentukannya, sebaran probabilitas dapat bersifat empirik atau bersifat teoretik. Sebaran empirik terbentuk dari hasil sensus atau mengambilan /contoh. Besar peluang yang terbentuk untuk setiap hasil tidak dapat diprediksi dan harus diturunkan dari hasil pengamatan. Teori statistika, tetapi demikian, lebih menyukai sebaran teoretik karena besar peluang dapat dihitung melalui fungsi yang sudah tertentu. Sebaran probabilitas teoretis tergantung dari macam data, apakah data itu non-numerik, diskret, atau peubah acak malar (continue). Data non-numerik, seperti jenis kelamin atau warna, akan memiliki sebaran probabilitas kategorik. Data yang terbentuk dari peubah acak diskret, seperti banyaknya rumah dalam suatu kampung atau , membentuk sebaran yang disebut . Data yang terbentuk dari distribusi acak malar menghasilkan sebaran yang disebut fungsi kepekatan probabilitas. * l * * s في علم الاحتمالات والإحصائيات، توزيع الاحتمال (بالإنجليزية: Probability distribution)‏ هو إعطاء احتمال معين لكل مجموعة جزئية قابلة للقياس من مجموعة نتائج تجربة عشوائية ما. وبتعبير آخر، هو قياس احتمالي مجاله تطبيق على مجموعة الأعداد الحقيقية. التوزيع الاحتمالي يعتبر حالة خاصة من مصطلح أكثر عمومية هو ، الذي يعتبر دالة تربط قيم احتمالات بمجموعات مقيسة من بحيث تحقق . كل متغير عشوائي ينشأعنه توزيع احتمالي يحتوي معظم المعلومات المهمة عن هذا المتغير. فاذا كان المتغير X متغيرا عشوائيا فان التوزيع الاحتمالي الموافق له ينسب للمجال [a, b] احتمالا : بمعنى أن احتمال أن يأخذ المتغير قيمة ضمن المجال هي : . يمكن وصف التوزيع الاحتمالي للمتغير عن طريق دالة التوزيع التراكمي التي تعرف كما يلي : نقول عن توزيع احتمالي أنه منقطع إذا كانت دال التوزيع التراكمي له مؤلف من تسلسل قفزات متناهية، مما يعني أنه يعود لمتغير عشوائي متقطع، وهو بالتعريف متغير يمكنه أن يأخذ فقط قيما من مجموعة محددة منتهية وقابلة للعد.و نقول عن التوزيع الاحتمالي أنه مستمر إذا كان دالة التوزيع التراكمي له مستمرة أي أنها تعود لمتغير عشوائي احتمال أخذه لقيمة محددة معينة معدوما أي : أيا كانت x من مجموعة الأعداد الحقيقية، في مثل هذه الحالة لا وجود لاحتمال غير معدوم إلا من أجل مجال ضمن مجموعة الأعداد الحقيقية اما ان يأخذ المتغير قيمة محددة فهو أمر عديم الاحتمال. هذه التوزيعات المستمرة المطلقة يمكن التعبير عنها بوساطة : دوال الكثاقة الاحتمالية : وهو عبارة عن دالة قابلة للتكامل بطريقة ليبيزغو، موجبة حتما ومعرفة على مجموعة الأعداد الحقيقية : Στις Πιθανότητες και στην Στατιστική, η κατανομή πιθανοτήτων αποδίδει την πιθανότητα σε κάθε μετρήσιμο υποσύνολο των πιθανών αποτελεσμάτων του τυχαίου πειράματος,της έρευνας, ή την διαδικασία της επαγωγικής στατιστικής. Παραδείγματα αποτελούν τα πειράματα των οποίων ο δειγματικός χώρος είναι μη-αριθμητικός, όπου η κατανομή θα είναι μια κατηγορική κατανομή. Πειράματα των οποίων ο δειγματικός χώρος αποτελείται από διακριτές τυχαίες μεταβλητές, όπου η κατανομή μπορεί να καθορίζεται από μια συνάρτηση συσσωρευμένης πιθανότητας.Τα πειράματα με δειγματικούς χώρους κωδικοποιούνται από συνεχείς τυχαίες μεταβλητές, όπου η κατανομή μπορεί να καθορίζεται από μια συνάρτηση πυκνότητας πιθανότητας. Πιο πολύπλοκα πειράματα, όπως εκείνα που αφορούν στοχαστικές διαδικασίες που ορίζονται σε συνεχή χρόνο, μπορεί να απαιτήσει τη χρήση των πιο γενικών μέτρων πιθανότητας. Στην εφαρμοσμένη πιθανότητα, μια κατανομή πιθανοτήτων μπορεί να οριστεί σε μια σειρά από διαφορετικούς τρόπους.Συχνά επιλέγεται για τη μαθηματική ευκολία: * Η παροχή μιας έγκυρης λειτουργία μάζα πιθανότητας ή πυκνότητας πιθανότητας * Η παροχή μιας έγκυρης αθροιστικής συνάρτησης συνάρτηση κατανομής * Η παροχή μιας έγκυρης συνάρτησης κινδύνου * Η παροχή μιας έγκυρης χαρακτηριστικής συνάρτησης * Η παροχή ενός κανόνα για την κατασκευή μιας νέας τυχαίας μεταβλητής από άλλες τυχαίες μεταβλητές των οποίων η κοινή πιθανότητα διανομής είναι γνωστή. Η κατανομή πιθανοτήτων μπορεί να είναι είτε μονοπαραγοντική είτε πολυπαραγοντική. Η μονοπαραγοντική κατανομή δίνει τις πιθανότητες μιας τυχαίας μεταβλητής, αναλαμβάνοντας διάφορες εναλλακτικές τιμές.Μια πολυμεταβλητή κατανομή (από κοινού κατανομή πιθανότητας) δίνει τις πιθανότητες ενός τυχαίου διανύσματος, ένα σύνολο από δύο ή περισσότερες τυχαίες μεταβλητές, αναλαμβάνοντας διάφορους συνδυασμούς των τιμών. Σημαντικές και συναντώνται συχνά οι κατανομές μονομεταβλητών πιθανοτήτων που περιλαμβάνουν την διωνυμική κατανομή, την εκθετική κατανομή και την κανονική κατανομή. Η πολυμεταβλητή κανονική κατανομή είναι μια συχνά απαντώμενη πολυμεταβλητή κατανομή. En teoría de la probabilidad y estadística, la distribución de probabilidad de una variable aleatoria es una función que asigna a cada suceso definido sobre la variable, la probabilidad de que dicho suceso ocurra. La distribución de probabilidad está definida sobre el conjunto de todos los sucesos y cada uno de los sucesos es el rango de valores de la variable aleatoria. También puede decirse que tiene una relación estrecha con las distribuciones de frecuencia. De hecho, una distribución de probabilidades puede comprenderse como una frecuencia teórica, ya que describe cómo se espera que varíen los resultados. La distribución de probabilidad está completamente especificada por la función de distribución, cuyo valor en cada x real es la probabilidad de que la variable aleatoria sea menor o igual que x. Em teoria da probabilidade e em estatística, uma distribuição de probabilidade descreve o comportamento aleatório de um fenômeno dependente do acaso. O estudo dos fenômenos aleatórios começou com o estudo dos jogos de azar – jogos de dados, sorteios de bolas de urna e cara ou coroa eram motivações para compreender e prever os experimentos aleatórios. Essas abordagens iniciais são fenômenos discretos, o que significa que o número de resultados possíveis é finito ou contável. Entretanto, certas questões revelam distribuições de probabilidade com suporte infinito não contável. Por exemplo, quando o lançamento de uma moeda tende ao infinito, o número de coroas aproxima-se de uma distribuição normal. Flutuações e variabilidade estão presentes em quase todo valor que pode ser medido durante a observação de um fenômeno, independente de sua natureza, além disso quase todas as medidas possuem uma parte de erro intrínseco. A distribuição de probabilidade pode modelar incertezas e descrever fenômenos físicos, biológicos, econômicos, entre outros. O domínio da estatística permite o encontro das distribuições de probabilidade adaptadas aos fenômenos aleatórios. Há muitas distribuições de probabilidade diferentes. Entre as distribuições de probabilidade, a distribuição normal tem uma importância particular. De acordo com o teorema central do limite, a distribuição normal aborda o comportamento assintótico de várias distribuições de probabilidade. O conceito de distribuição de probabilidade é formalizado matematicamente pela teoria da medida – uma distribuição de probabilidade é uma medida muitas vezes vista como uma distribuição que descreve o comportamento de uma variável aleatória discreta ou contínua. Uma medida é uma distribuição de probabilidade se sua massa total for 1. O estudo de uma variável aleatória de acordo com uma distribuição de probabilidade discreta revela o cálculo de somas e de séries, enquanto que o estudo de uma variável aleatória de acordo com uma distribuição de probabilidade absolutamente contínua revela o cálculo de integrais. As funções particulares permitem caracterizar as distribuições de probabilidade como a função de distribuição e a função característica. 確率分布(かくりつぶんぷ、英: probability distribution)は、確率変数に対して、各々の値をとる確率全体を表したものである。日本産業規格では、「確率変数がある値となる確率,又はある集合に属する確率を与える関数」と定義している。 Probabilitate teorian eta estatistikan, probabilitate-banaketa batek zorizko aldagai batek har ditzakeen balioak, balio hauei dagokien probabilitateekin batera, ezartzen ditu. Probabilitate banaketa diskretuak eta jarraiak izan daitezke. Diskretua edo jarraitua den, probabilitate banaketa era ezberdinetan definitzen da. In de kansrekening speelt het begrip kansverdeling, waarschijnlijkheidsverdeling of -distributie (niet te verwarren met de distributie in de analyse) een centrale rol. Bij een experiment waarin het toeval een rol speelt, geeft de kansverdeling aan hoe "de kansen verdeeld zijn", d.w.z. wat de kans is op ieder van de verschillende, mogelijke uitkomsten. In de theorie wordt hier een specifieke betekenis aan gegeven: de 'kansverdeling' duidt op het geheel van mogelijke uitkomsten en de bijbehorende kansen. Een voorbeeld van een dergelijk experiment is een worp met een zuivere dobbelsteen. De kansverdeling van het geworpen aantal ogen wordt beschreven als gelijk aan 1/6 voor elke uitkomst. Strikt genomen is dit echter de kansfunctie, waarmee overigens de kansverdeling wel vastgelegd wordt. Het formele begrip kansverdeling is voornamelijk van theoretisch belang en zelfs daar zal in het geval van een stochastische variabele vaker met de verdelingsfunctie, die geheel bepalend is voor de kansverdeling, gewerkt worden. Bij discrete kansverdelingen wordt de verdelingsfunctie op zijn beurt weer geheel bepaald door een kansfunctie en bij continue veranderlijken (absoluut continue verdelingsfunctie) door een kansdichtheid. In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space). For instance, if X is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of X would take the value 0.5 (1 in 2 or 1/2) for X = heads, and 0.5 for X = tails (assuming that the coin is fair). Examples of random phenomena include the weather conditions at some future date, the height of a randomly selected person, the fraction of male students in a school, the results of a survey to be conducted, etc. 확률 분포(確率 分布, probability distribution)는 확률 변수가 특정한 값을 가질 확률을 나타내는 함수를 의미한다. 예를 들어, 주사위를 던졌을 때 나오는 눈에 대한 확률변수가 있을 때, 그 변수의 확률분포는 이산균등분포가 된다. 확률 분포는 확률 변수가 어떤 종류의 값을 가지는가에 따라서 크게 와 중 하나에 속하며, 둘 중 어디에도 속하지 않는 경우도 존재한다. En matematiko kaj statistiko, probablodistribuo aŭ probablodenso estas asigno de probablo al ĉiu intervalo de la reelaj nombroj, tiel ke la estas kontentigita. En teknika terminoj, probablodistribuo estas probablo kies domajno estas la sur la reelaj nombroj. La probablodistribuo indikas, kiel la probableco dividiĝas inter la eblaj hazardaj rezultoj, aparte la eblaj rezultoj de hazarda variablo.La statistiko kvante mezuras la hazardon kaj estas la teoria kontraŭparto de la empiria oftecodistribuo, kiu rezultiĝas el analizo de reale havigitaj mezuraj rezultoj. Unu el multaj aplikoj de probablodistribuo estas pritakso de riskoj en la asekura industrio. Probablodistribuo estas speciala okazo de la pli ĝenerala nocio de probablo, kiu estas funkcio kiu asignas probablojn, kontentigantajn la aksiomojn de Kolmogorov, al mezureblaj aroj de mezurebla spaco. Ĉiu hazarda variablo donas probablodistribuon, kaj ĉi tiu distribuo enhavas plejparton de la grava informo pri la variablo. Se X estas hazarda variablo, la korespondanta probablodistribuo asignas intervalo [a, b] la probablon Pr[a ≤ X ≤ b], kio estas la probablo ke la variablo X estos prenos valoron en la intervalo [a, b]. En théorie des probabilités et en statistique, une loi de probabilité décrit le comportement aléatoire d'un phénomène dépendant du hasard. L'étude des phénomènes aléatoires a commencé avec l'étude des jeux de hasard. Jeux de dés, tirage de boules dans des urnes et jeu de pile ou face ont été des motivations pour comprendre et prévoir les expériences aléatoires. Ces premières approches sont des phénomènes discrets, c'est-à-dire dont le nombre de résultats possibles est fini ou dénombrable. Certaines questions ont cependant fait apparaître des lois à support infini non dénombrable ; par exemple, lorsque le nombre de tirages de pile ou face effectués tend vers l'infini, la répartition des fréquences avec lesquelles le côté pile apparaît s'approche d'une loi normale. Des fluctuations ou de la variabilité sont présentes dans presque toute valeur qui peut être mesurée lors de l'observation d'un phénomène, quelle que soit sa nature ; de plus presque toutes les mesures ont une part d'erreur intrinsèque. Les lois de probabilités permettent de modéliser ces incertitudes et de décrire des phénomènes physiques, biologiques, économiques, etc. Le domaine de la statistique permet de trouver des lois de probabilités adaptées aux phénomènes aléatoires. Il existe beaucoup de lois de probabilités différentes. Parmi toutes ces lois, la loi normale a une importance particulière puisque, d'après le théorème central limite, elle approche le comportement asymptotique de nombreuses lois de probabilités. Le concept de loi de probabilité se formalise mathématiquement à l'aide de la théorie de la mesure : une loi de probabilité est une mesure, souvent vue comme la loi décrivant le comportement d'une variable aléatoire, discrète ou continue. Une mesure est une loi de probabilité si sa masse totale vaut 1. L'étude d'une variable aléatoire suivant une loi de probabilité discrète fait apparaître des calculs de sommes et de séries, alors que si sa loi est absolument continue, l'étude de la variable aléatoire fait apparaître des calculs d'intégrales. Des fonctions particulières permettent de caractériser les lois de probabilité, par exemple la fonction de répartition et la fonction caractéristique.
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