Prove Theorem 6.1 starting with Theorem 6.2. (Hint: Refer to the section onorder statistics in Chapter 3.)

STAT 2004 WEEK 9 BERNOULLI DISTRIBUTION In a Bernoulli distribution, an outcome has two possibilities: success or failure. o Success- What we were interested in happened. o Success is represented by a 1, while failure is represented by a 0. Probability of success is represented by a p. For a Bernoulli random variable. o X ~ Bernoulli (p) o The expectation of a Bernoulli distribution = the probability of success. (E[X]=p) o Variance [X] = p (1-p) o SD [X] = the square root of the variance Categorical nominal: o You can put the number of successes and failures into a bar plot. BINOMIAL DISTRIBUTION 0 1 When