Suppose you play a strange game where you flip a fair coin k times. If the...

 

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Suppose you play a strange game where you flip a fair coin k times. If the coin comes up heads on the ith flip, you win 20i dollars and otherwise you lose 412 dollars (for all i such that 1ik). Let X, be a random variable denotes the amount of money you win from the ith flip (losing money can be thought of as "winning" negative money). Let X be a random variable denotes the amount of money you win across all k of your flips. (1) (0.5 points) Compute the expected value of X1. E(X1)= (2) (0.5 points) Give a general formula for the expected value of the random variable X, (where 1 ik). E(X) = (3) (0.5 points) Describe the random variable X as the sum of k random variables. X = Suppose you play a strange game where you flip a fair coin k times. If the coin comes up heads on the ith flip, you win 20i dollars and otherwise you lose 412 dollars (for all i such that 1ik). Let X, be a random variable denotes the amount of money you win from the ith flip (losing money can be thought of as "winning" negative money). Let X be a random variable denotes the amount of money you win across all k of your flips. (1) (0.5 points) Compute the expected value of X1. E(X1)= (2) (0.5 points) Give a general formula for the expected value of the random variable X, (where 1 ik). E(X) = (3) (0.5 points) Describe the random variable X as the sum of k random variables. X =