STAT 3460 Lecture Notes - Lecture 5: Probability Mass Function, Bernoulli Trial, Random Variable
14 Mar 2016
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Bernoulli trial an experiment in which there are only two possible outcomes; one labeled. The probability of success is denoted by p. Binomial distribuion the distribuion of the number of successes in a series of bernoulli trials. Assume that a series of n bernoulli trials is conducted, each with the same success probability p. assume further that the trials are independent. Let the random variable x equal the number of successes in these n trials. Then x is said to have the binomial distribuion with parameters n and p (x ~ bin(n,p): probability mass funcion of a binomial random variable. If x ~ bin(n,p), the probability mass funcion of x is p(x) = p(x = x) = x (1 p) n! p x! (n x)! n x x = 0, 1, , n. There are three arrangements of two heads in three tosses of a coin: hht, hth, thh. P(x = 2) = p(hht or hth or thh)
