Proof | 動物用藥查詢網
2020年5月11日—Proof:Probabilitymassfunctionofthebinomialdistribution...Theorem:LetXXbearandomvariablefollowingabinomialdistribution:X∼Bin( ...
Index: The Book of Statistical Proofs[1] ▷ Probability Distributions[2] ▷ Univariate discrete distributions ▷ Binomial distribution ▷ Probability mass functionTheorem: Let $X$ be a random variable[3] following a binomial distribution[4]:
[label{eq:bin} X sim mathrm{Bin}(n,p) ; .]Then, the probability mass function[5] of $X$ is
[label{eq:bin-pmf} f_X(x) = {n choose x} , px , (1-p){n-x} ; .]Proof: A binomial variable[6] is defined as the number of successes observed in $n$ independent[7] trials, where each trial has two possible outcomes[8] (success/failure) and the probability[9] of success and failure are identical across trials ($p$, $q = 1-p$).
If one has obtained $x$ successes in $n$ trials, one has also obtained $(n-x)$ failures. The probability of a particular series of $x$ successes and $(n-x)$ failures, when order does matter, is
Binomial distribution | 動物用藥查詢網
1.3.6.6.18. Binomial Distribution | 動物用藥查詢網
Lesson 10 | 動物用藥查詢網
Probability Mass Function | 動物用藥查詢網
Formulas | 動物用藥查詢網
3.2.5 Negative Binomial Distribution | 動物用藥查詢網
Binomial Distribution Example (2 of 3 | 動物用藥查詢網
Proof | 動物用藥查詢網
Binomial Distribution | 動物用藥查詢網
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