The joint probability density function of X and Y is given b

The joint probability density function of X and Y is given by (a) Find the marginal densities of X and of Y. Identify the distributions.

Solution

This is normal distribution combined when x and y are independent.

x is normal with mux, and sigma x while y is normal with mu y and sigma y

Marginal distribution of X is normal distribution of X with mean mux and std dev sigma x

and of y is normal with mean muy and std dev sigma y.