STAT 400 Lecture Notes - Lecture 1: Binomial Distribution, Bernoulli Trial, Random Variable

• School: University of Maryland
• Department: Statistics and Probability
• Course: STAT 400
• Professor: Tim Pilachowski

Document Summary

Stat 400, section 3. 4 the binomial probability distribution. Definition of bernoulli trials which make up a binomial experiment: The number of trials, n, in an experiment is fixed in advance. There are exactly two events/outcomes for each trial, usually labeled success (s) and failure (f). Trials are independent from one trial to the next, i. e. the outcome of one trial doesn"t affect the next. P(s) = p must be the same for each trial. [p(f) = 1 p is often designated as q]. P(s) = p is the same for each trial? p = Let random variable x = number of successes, i. e. number of blues picked. x. For a binomial distribution n trials, p(s) = p, x = number of successes, x = 0, 1, 2, , n. Semi-important: in the real world, sampling with replacement is not always possible.