Question

Consider the normal random variable Z′ ∼ N(15, 40). Specify the mean E[Z′] and variance Var(Z′) of the random variable Z′. Explain.

Answer 1

The mean of Z' is 15 and the variance is 40.

Step-by-step explanation:

The mean, denoted by E[Z'], of a normal random variable is equal to its given mean. In this case, the mean of Z' is 15.

The variance, denoted by Var(Z'), of a normal random variable is equal to the square of its given standard deviation. In this case, the standard deviation is the square root of the given variance, which is √(40) = 2√(10). Therefore, the variance of Z' is (2√(10))^2 = 40.