# Expected value of bivariate pdf

• boneill3

#### boneill3

Is the expected value E[x]or E[y] of a bivariate pdf fXY(xy)

\int x f(x,y)dx

or

E[y]

\int y f(x,y)dy ?

example if f(x,y) = x+y

E[X] = \int x *(x+y)dx

regards
Brendan

You need to carry out the double integral. A single integration gives the conditional expection of one variable with rexpect to the other.

So just say you had the lmits of 0<x<1 0<y<1
The expected value would be:
$E[X] = \int_{0}^{1}\int_{0}^{1} x *(x+y)dxdy = 7/12 [\latex] Is that right? Sorry, [itex] E[X] = \int_{0}^{1}\int_{0}^{1} x *(x+y)dxdy = 7/12$

regards

## 1. What is the expected value of a bivariate PDF?

The expected value of a bivariate PDF (probability density function) is a measure of the central tendency or average value of a bivariate random variable. It represents the point at which the bivariate PDF is balanced and is calculated by multiplying each possible value of the random variable by its probability and summing up all the products.

## 2. How is the expected value of a bivariate PDF calculated?

The expected value of a bivariate PDF is calculated by taking the integral of the product of the two variables over the entire range of possible values. This can be expressed mathematically as E(X,Y) = ∫∫xyp(x,y)dxdy, where p(x,y) is the bivariate PDF.

## 3. What does the expected value of a bivariate PDF tell us?

The expected value of a bivariate PDF provides us with a single number that summarizes the distribution of a bivariate random variable. It represents the most likely outcome or average value of the two variables considered together.

## 4. Is the expected value of a bivariate PDF the same as the mean?

Yes, the expected value of a bivariate PDF is the same as the mean. However, the term "expected value" is used for continuous random variables, while "mean" is used for discrete random variables.

## 5. Can the expected value of a bivariate PDF be negative?

Yes, the expected value of a bivariate PDF can be negative. This means that the distribution of the bivariate random variable is skewed to the left, with most values falling below the expected value. It is also possible for the expected value to be zero or positive, depending on the distribution of the variables.