Question

(1 point) Consider n=20 independent flips of a fair coin. Say that a changeover occurs whenever an outcome differs from the one preceding it. For example, if n=6 and the outcome is T H T T H T, then there is a total of 4 changeovers. Find the expected number of changeovers for n=20. Answer =

Answer 1

9.5

Explanation:

There is no changeover in the first throw. The probability of each changeover is 1/2 and it doesnt depend on the other changeovers. The only thing that modifies each experiment is the result of the previous flip, but regardless of weather it was tails or heads, the probability will always be 1/2.

Since the coin is flipped 20 times and the first time there is no changeover, there are a total of 19 experiments. All of them independent and with probability 1/2. Therefore, the total amount of changeovers for 20 flips is a random variable with distribution Binomial B(19,0.5), the expected value of a Binomial B(n,p) is n*p. In this case, the expected value of changeovers for n=20 is 19*0.5 = 9.5.