Question

The random variable Z denotes a standard normal random variable, Z∼N(0,1). What is the distribution of the random variable μ+σZ ? Choose the correct answer below. A. N(μ,σ² ) B. P(Z<1) C. σ² D. μ

Answer 1

The distribution of the random variable μ+σZ is N(μ,σ²).

Step-by-step explanation:

The distribution of the random variable μ+σZ is A. N(μ,σ²). When we add a constant value to a normal distribution, the mean of the resulting distribution will also be shifted by that constant. Similarly, the standard deviation of the resulting distribution will remain the same.

Therefore, when we add μ+σZ, the resulting distribution will have a mean of μ and a standard deviation of σ, which is represented as N(μ,σ²).