flips a fair coin until a tail first appears, and if the number of tosses equals m, then Tom gets a payoff for 2 m pounds. Calculate the expected value of his payoff.

the expected value of Tom's payoff is m²

Step-by-step explanation:

Given the data in the question,

E[x] = mp                                        

where p = 1/2

Now Tom gets payoff pounds until a tail first appears = 2m pounds

so

E[x] = m × 1/2 × 2m

E[x] = m²

Therefore the expected value of Tom's payoff is m²