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Expected Value and First Order Stochastic Dominance

by odck11
Tags: means, stochastic dominance
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odck11
#1
Feb4-13, 03:21 PM
P: 2
Dear All:

Given two random variables X and Y, if I have established the relationship E[X]>=E[Y], does this necessarily imply that X must have a first-order-stochastic dominance over Y?

I know that first order stochastic dominance implies that the mean value of the dominating random variable be greater than the other variable but I am trying to find out whether the reverse must hold.

Thanks in advance.
Regards.
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mathman
#2
Feb4-13, 03:30 PM
Sci Advisor
P: 6,040
Quote Quote by odck11 View Post
Dear All:

Given two random variables X and Y, if I have established the relationship E[X]>=E[Y], does this necessarily imply that X must have a first-order-stochastic dominance over Y?

I know that first order stochastic dominance implies that the mean value of the dominating random variable be greater than the other variable but I am trying to find out whether the reverse must hold.

Thanks in advance.
Regards.
Not necessarily. Let X have two states 10 and 0, while Y has two states 2 and 1, both with equal probability. E(X) = 5, E(Y) = 1.5, but X does not dominate Y.
odck11
#3
Feb4-13, 03:46 PM
P: 2
Great! Thanks a lot. That's what I guessed too but just wanted to make sure. I appreciate your fast reply.


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