DISCRETE DISTRIBUTIONS

LINEAR FUNCTION OF A RANDOM VARIABLE

If x is a random variable and a and b are numerical constants, then the random variable y is defined by

andbxay

)()(;

)()()(2 XSDbYSDVarXbVarY

XbEabXaEYE

Let x be the number of gallons required to fill a propane tank. Suppose that the mean and standard deviation is 318 gal. and 42 gal., respectively. The company is considering the pricing model of a service charge of $50 plus $1.80 per gallon. Let y be the random variable of the amount billed. What is the mean and standard deviation for the amount billed?m = $622.40 & s = $75.60

LINEAR COMBINATIONS

n

n

n

i

n

VarXVarXVarXYSD

VarXVarXVarXVarY

EXEXEXEY

X

XXXY

....)(

....

....

thentindependenarealland

...If

21

21

21

21

A nationwide standardized exam consists of a multiple choice section and a free response section. Each score is independent, and the mean and standard deviation are reported:

mean SD

MC 38 6

FR 30 7

If the test score is computed by adding the multiple choice and free response, then what is the mean and standard deviation of the test?

=m 68 & s = 9.2195