Question

marginal probability density functions of X and Y are the integral of F(x, y) integrated in terms of y to find f(x) and integrated in terms of x to find f(y)

Answer 1

To find the marginal probability density functions of X and Y, we integrate the joint probability density function (F(x, y)) in terms of y to find f(x) and integrate it in terms of x to find f(y).

Step-by-step explanation:

A marginal probability density function represents the probability distribution of a single random variable. To find the marginal probability density functions of X and Y, we need to integrate the joint probability density function (F(x, y)) in terms of y to find f(x) and integrate it in terms of x to find f(y).

For example, to find f(x), we integrate F(x, y) with respect to y over the entire range of y values. This gives us the marginal probability density function f(x) for the variable X.

To find f(y), we integrate F(x, y) with respect to x over the entire range of x values. This gives us the marginal probability density function f(y) for the variable Y.