Example

Let us find out the expected value of the continuous PDF given in Example 3.

Properties of Expected Values

1. The expected value of a constant is the constant itself. Thus, if b is a constant, E(b) = b.

2. If a and b are constants,

This can be generalized. If Xi, X2,..., XN are N random variables and ai, a2,..., aN and b are constants, then

E(ai Xi + a2 X2 + ■ ■ ■ + aNXN + b) = ai E(Xi) + a2 E(X2) + ••• + aNE(XN) + b

3. If X and Y are independent random variables, then

That is, the expectation of the product XY is the product of the (individual) expectations of X and Y.

4. If X is a random variable with PDF f(x) and if g(X) is any function of X, then

880 APPENDIX A: A REVIEW OF SOME STATISTICAL CONCEPTS

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