Question

Suppose you flip a fair coin until it lands heads up for the first time. It can be shown (do not try to calculate this) that the expected value of the number of flips required is 2. Explain (with a sentence or two) what this expected value means in this context.

Answer 1

Expected value or also called as expectation is the mean value we get if we repeat the experiment many times

In our context the coin is fliped till it lands heads

The success is considered only if we get heads

So this clearly follows a Geometric distribution

For a geometric distribution

Expectation = 1/p

where p = probability of success

For a coin toss of head we have p = 0.5

Expectation = 1/p = 1/0.5 = 2

So this means that if the experiment we to be repeated the coin toss many time we need atleast 2 tosses on average to get a head