# Calculation of expected value of 2RVs

• nikozm
In summary, the expected value of 2 random variables is a measure of the average value that can be expected from the combination of the two variables. It is calculated by multiplying each possible value of one variable with the corresponding probabilities of the other variable, and then summing them up. This formula can be written as E(X,Y) = ∑x∑yp(x,y), where x and y are the possible values of the two variables and p(x,y) is the joint probability of those values occurring. It represents the average value that can be expected from the combination of the two variables and is often used in decision making to assess potential outcomes and risks associated with a choice. The expected value can be negative, indicating a higher likelihood of
nikozm
Hello, i was wondering if the following is correct:

The expected value of (a*x+b*x*y)/(c*y) given that a,b,c are positive constants and x,y are positive random variables is:

∫∫(a*x+b*x*y)/(c*y)*f_{x}(x)*f_{y}(y)dydx (where f_{z}(.) is the PDF of z).

It is correct as long as x and y are independent.
If not you need g(x,y) as the joint density not fx(x)fy(y).

## What is the expected value of 2 random variables?

The expected value of 2 random variables is a measure of the average value that can be expected from the combination of the two variables. It is calculated by multiplying each possible value of one variable with the corresponding probabilities of the other variable, and then summing them up.

## How is the expected value of 2 random variables calculated?

The expected value of 2 random variables is calculated by multiplying each possible value of one variable with the corresponding probabilities of the other variable, and then summing them up. This formula can be written as E(X,Y) = ∑x∑yp(x,y), where x and y are the possible values of the two variables and p(x,y) is the joint probability of those values occurring.

## What does the expected value of 2 random variables represent?

The expected value of 2 random variables represents the average value that can be expected from the combination of the two variables. It is a useful measure for decision making and risk assessment.

## Can the expected value of 2 random variables be negative?

Yes, the expected value of 2 random variables can be negative. This indicates that the combination of the two variables is more likely to result in a loss rather than a gain. However, a negative expected value does not necessarily mean that the outcome will be negative, as it is based on probabilities and not certain outcomes.

## How is the expected value of 2 random variables used in decision making?

The expected value of 2 random variables is often used in decision making to assess the potential outcomes and risks associated with a particular choice. It can help to determine the best course of action by weighing the potential gains and losses of each option.

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