The expected value of a random variable X is 10 and the standard deviation is 2. The standard deviation of the random variable Y = 2X - 10 is:
A)2
B)4
C)-10
D)-6

Question

Quizplus · Accepted Answer

If Y = 2X - 10, we can find the expected value and variance of Y using the following formulas:

E(Y) = E(2X - 10) = 2E(X) - 10 = 2(10) - 10 = 10

Var(Y) = Var(2X - 10) = 4Var(X) = 4(2^2) = 16

Therefore, the standard deviation of Y is the square root of the variance, which is:

SD(Y) = sqrt(16) = 4

So the answer is B, 4.

The Expected Value of a Random Variable X Is 10