Hi
There is a bag containing numbers from 1 to n. A number is drawn at random from the bag and put back.(let the number be "X") A second number is drawn after that. (let the number be "Y")
THe person gets 10$ if X>y, he has to pay 5$ is x<y and gets 0$ is x=y.
What is the expected payoff of the game?
(PS: I am not sure how to calculate the probabilities of x>y,x<y). The prob of x=y should be 1/n^2 most probably but not sure.. Any help is appreciated)
Thanks
Hello, champrock!
There are: . possible draws.There is a bag containing numbers from
A number is drawn at random from the bag and put back. (Let the number be .)
A second number is drawn after that. (Let the number be .)
The player: .
What is the expected payoff of the game?
In cases, the numbers are equal.
. .
Among the other cases, half of them have greater than
That is, in cases,
. . Hence: .
Similarly: .
Therefore: .
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
Translation: .
On the average, you can expect to win slightly less than $2.50 per game.