Question

If X is a random variable with expected value 2, then the expected value of 5X will be:______

Answer 1

E(5X) = 10

Explanation:

The expected value of a random variable X is denoted as; E(X)

Now we are told it's equal to 2.

Thus;

E(X) = 2

Now, we want to find the expected value of 5X

We will use the principle from expected value derivations below;

E(cX + d) = cE(X) + d

Also;

If E(X) = z

Then;

E(aX) will give; aE(X) = az

From our question, we have;

E(X) = 2

Thus;

E(5X) = 5E(X) = 5 × 2 = 10