Suppose you toss a coin and it you win a dollar if it comes up heads. If it comes up tails you toss the coin again. This time you get two dollars if it is heads. If it is tails you toss it again. This time you win four dollars if it is heads, but if it is tails you toss it again. Continue in this fashion fora toatl of 10 flips of the coin, after which you get nothing if it is tails. What is the mathematical expectation for this game?
probability of winning one dollar = .5
of $2 = .5*.5* = .25
of $3 = .5^3
of $4 = .5^4
so E = .5*1 + .25*2 + .125*3 ..... .5^10 *10
posted by Damon