Explore BrainMass

Explore BrainMass

    St Petersburg Paradox - Random variables

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    This is a two part problem that expands on the St Petersburg Paradox. I have attempted this problem and ca not seem to arrive at the answers given in my book. (a) c/2-c (b) 2 log2

    Below is the problem
    A fair coin is flipped until the first tail appears; we win $2 if it appears on the first toss, $4 on the second and in general $2^k if it first appears on the kth toss. Let the random variable X denote our winnings. How much should we pay in order for this to be a fair game.++++++++++

    I have already figured out the paradoxical nature of this part of the problem. That the series is divergent. Now where I'm having the trouble is
    (a)what if the amounts won are c^k instead of 2^k where 0<c<2
    (b) the amounts won are log 2^k

    © BrainMass Inc. brainmass.com September 24, 2022, 6:56 pm ad1c9bdddf

    Solution Preview

    p= probability of winning = 1/2
    hence of losing = q = 1 -1/2
    expectations of winning:
    E(X) = (1/2)*2 + (1- 1/2)*(1/2)*4 + (1- 1/2)*(1- 1/2)*(1/2)*2^3 + ....
    => E(X) = 1+1+1+1+1+.... infinity = infinity
    because, ...

    Solution Summary

    The expert examines St. Petersburg paradox for random variables. The solution answers the question(s) below.