Expected Value and First Order Stochastic Dominance

In summary, the conversation discusses the relationship between two random variables, X and Y, and whether establishing that E[X]>=E[Y] necessarily implies that X must have a first-order-stochastic dominance over Y. It is clarified that this is not always the case and an example is provided to support this. The conversation ends with gratitude for the fast reply and confirmation of the initial guess.
  • #1
odck11
2
0
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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  • #2
odck11 said:
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.
 
  • #3
Great! Thanks a lot. That's what I guessed too but just wanted to make sure. I appreciate your fast reply.
 

1. What is expected value?

Expected value is a mathematical concept used to calculate the average outcome of a random event over a large number of trials. It is calculated by multiplying each possible outcome by its probability and summing them together.

2. How is expected value used in decision making?

Expected value is used in decision making to help determine the most rational choice between different options. By calculating the expected value for each option, the option with the highest expected value can be chosen.

3. What is first order stochastic dominance?

First order stochastic dominance is a concept used to compare the risk or uncertainty associated with different outcomes. It states that if one option has a higher expected value and less variability than another option, then it dominates the other option in terms of risk.

4. How is first order stochastic dominance related to expected value?

First order stochastic dominance is related to expected value because expected value is one of the factors that is used to determine whether one option dominates another. If one option has a higher expected value and less variability, it will also have first order stochastic dominance over the other option.

5. Can expected value and first order stochastic dominance be applied to all types of decisions?

Yes, expected value and first order stochastic dominance can be applied to any decision that involves risk or uncertainty. This includes business decisions, investment decisions, and even personal decisions.

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