Question

If X and Y are two random variables, with E(X)=6 and E(Y)=9, then E(2X+2Y is

a) 39
b) 30
c) 27
d) None of the above

Answer 1

The expected value of 2X+2Y is 30.

Step-by-step explanation:

The expected value of a random variable is calculated by taking the weighted average of all possible values it can take on, where the weights are the probabilities of those values. In this case, we have E(2X+2Y), so we need to calculate the expected value of 2X and the expected value of 2Y separately, and then add them together.

Using the linearity of expectation, we can multiply the constant 2 by the expected values of X and Y respectively. So, E(2X) = 2 * E(X) = 2 * 6 = 12, and E(2Y) = 2 * E(Y) = 2 * 9 = 18.

Finally, we add the two expected values together: E(2X+2Y) = E(2X) + E(2Y) = 12 + 18 = 30.