Problem 6: The expected value of a geometric random variable with success parame

Question

Problem 6: The expected value of a geometric random variable with success parameter p is equal to 1/p. In order to assess whether this result is intuitive, answer the following: (a) For a fair coin, under the frequency interpretation of probability, on average, what is the number of times that you have to flip the coin until the first head appears? (b) If the probability of heads 0.01 for a coin, then, on average, what is the number of times that you have to flip the coin until the first head appears? (Now, think about whether the expected value of a geometric random variable 1/p is intuitive to you.)

Explanation / Answer

a) Here success is Head appear on the flip of a coin

For the fair coin P(head) = P(Tail) = 0.5

So for the first success the expected number of flips needed as 1/0.2 = 2 .

b) for suppose p = probability of head is appear = 0.01

for the first success the expected number of flips needed as 1/p = 1/ 0.01 = 100

So we need an average 100 flips for the first success.

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