g Suppose I will flip a fair coin until it lands Heads for the first time, and you will receive $2 if the game lasts for 1 round, $4 if the game lasts for 2 rounds, $8 if the game lasts for 3 rounds, and in general, $2n if the game lasts for n rounds. How much would you be willing to pay to play this game once

Step-by-step explanation:

The main idea is that I would like to pay less than what I'm expecting to win, so in that way, I get a profit out of playing this game. Let X be the number of tosses until I get a Heads. By definition, this is a geometric random variable with parameter p = 1/2.

Let Y the amount I received for playing. So, we want to calculate the expected value of Y.

We can calculate it as follows

Since X is a geometric random variable, we have that

Then,

So, we expect to have an infinite amount. Given this, we can pay as much as we want to play the game.

the answer is b i just did that

step-by-step explanation:

answer: 2530

hope this