Joint probability distributions of three or more random variables can be interpreted by extending the ideas in this section. I-'or example, suppose that three continuous random variables X, Y, and Z have a joint probability density function
f(x, y, z) = 3xyz2/32
for 0 (a) Establish that this is a valid joint probability density function by showing that it is always positive within the state space 0 (b) In general.

What is p(0 (c) The marginal probability density function of a particular random variable can be calculated from f joint probability density function by integrating over all values of the other random variables. What is the marginal probability density function of the random variable X?

Pa s X sb.esYsd.eszs f(x,y,z)dxdydz