STAT_333_Assignment_1

STAT_333_Assignment_1 - STAT 333 Assignment 1 Due:...

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STAT 333 Assignment 1 Due: Thursday, May 29 at the beginning of class 1. Consider 10 independent coin flips having probability p of landing heads. We say a changeover occurs whenever an outcome differs from the one preceding it. For example, if the results of the flips are H H T H T H H T then there are five changeovers. a. Find the expected number of changeovers. b. Find the variance of the number of changeovers. c. Describe how the mean and variance of the number of changeovers behave for different values of p . Provide a brief logical explanation. (Hint: attach indicator variables to pairs of consecutive flips. X 1 for 1 st and 2 nd , X 2 for 2 nd and 3 rd , etc.) 2. Suppose we have a series of independent trials, where the outcome is either S or F, but the probability of S on trial n is p n , not necessarily constant. This is different from Bernoulli trials, where all p n = p . Let X = number of trials until the first S, including that trial. (Similar to Geometric) a. Give an expression for the probability mass function, P(X =
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