Question

Suppose that X and Y are independent random variables having the joint probability distribution. Find: (E(2X - 3Y)); (E(XY)).

A. E(2X - 3Y) = 2E(X) - 3E(Y)); (E(XY) = E(X)E(Y)
B. E(2X - 3Y) = 2E(X) - 3E(Y)); (E(XY) = E(X + Y)
C. E(2X - 3Y) = E(X) - E(Y)); (E(XY) = E(X) + E(Y)
D. E(2X - 3Y) = E(X + Y)); (E(XY) = 2E(X) - 3E(Y)

Answer 1

The correct expectations for the independent random variables X and Y are E(2X - 3Y) = 2E(X) - 3E(Y) and E(XY) = E(X)E(Y), which corresponds to Option A.

Step-by-step explanation:

The calculations involving expected values of independent random variables can be done using the linearity of expectation and properties of independent events. Let's solve for the expected values given in the options.

E(2X - 3Y)

By linearity of expectation, we can say E(2X - 3Y) = E(2X) - E(3Y) = 2E(X) - 3E(Y).

E(XY)

Since X and Y are independent, the expected value of their product is the product of their expected values: E(XY) = E(X)E(Y).

Therefore, the correct option which represents these calculations is:

Option A: E(2X - 3Y) = 2E(X) - 3E(Y), E(XY) = E(X)E(Y)