Expected Value and First Order Stochastic Dominance

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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.
 

mathman

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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.
 
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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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