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


Was this article helpful?

0 0
Rules Of The Rich And Wealthy

Rules Of The Rich And Wealthy

Learning About The Rules Of The Rich And Wealthy Can Have Amazing Benefits For Your Life And Success. Discover the hidden rules and beat the rich at their own game. The general population has a love / hate kinship with riches. They resent those who have it, but spend their total lives attempting to get it for themselves. The reason an immense majority of individuals never accumulate a substantial savings is because they don't comprehend the nature of money or how it works.

Get My Free Ebook

Post a comment