probability and statistics

Question

You toss independently a fair coin and you count the number of tosses until the first tail appears. If this number is n, you receive 2n dollars. What is the expected amount that you will receive? How much would you be willing to pay to play this game?

Answer 1

You could calculate the expectation value for getting tails on the 1,2,3...n... try up to infinity and sum the results.

 

The integral test indicates the sum does converge.  The exact sum I believe is 4.

Answer 2

First set up a table with columns; one each for  n, P(n), 2n , (2n)P(n).

 

Using than table You can calculate the expected amount.

 

When you have that table set up if you don't know the next step comment back with the first 4 rows of the table and I'll go to the next step.