Consider the following density function:

It can be readily verified that f(x) > 0 for all x in the range 0 to 3 and that /03 1 x2dx = 1. (Note: The integral is (27x3 |0) = 1.) If we want to evaluate the above PDF between, say, 0 and 1, we obtain /J 9x2dx = (57x3 |J) = 57! that is, the probability that xlies between 0 and 1 is 1/27.

FIGURE A.2 Density function of a continuous random variable.

© The McGraw-H Companies, 2004


Joint Probability Density Functions

Discrete Joint PDF. Let X and Ybe two discrete random variables. Then the function f (x, y) = P(X = x and Y = y)

= 0 when X = x and Y = y is known as the discrete joint probability density function and gives the (joint) probability that X takes the value of x and Y takes the value of y.

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