Expected Value and First Order Stochastic Dominance

[odck11]

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]

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]

Great! Thanks a lot. That's what I guessed too but just wanted to make sure. I appreciate your fast reply.