Monday, March 4, 2013

Expected Value & Variance




Consider a lottery with three possible outcomes:
    $125 will be received with probability 0.2
    $100 will be received with probability 0.3
    $50 will be received with probability 0.5 



a.   What is the expected value of the lottery?

b.   What is the variance of the outcomes?

c.   What would a risk-neutral person pay to play the lottery?



















ANSWER
a.   What is the expected value of the lottery?
The expected value, EV, of the lottery is equal to the sum of the returns weighted by their probabilities:
EV = (0.2)($125) + (0.3)($100) + (0.5)($50) = $80.
b.   What is the variance of the outcomes?
The variance, s2, is the sum of the squared deviations from the mean, $80, weighted by their probabilities:
s2 = (0.2)(125 - 80)2 + (0.3)(100 - 80)2 + (0.5)(50 - 80)2 = $975.
c.   What would a risk-neutral person pay to play the lottery?
A risk-neutral person would pay the expected value of the lottery: $80.


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