Question

Find the item that matches the description below. The random variable X denotes a normally distributed random​ variable, X~N(μ, σ2). The random variable Z denotes a standard normal random​ variable, Z~N(0, 1).

Variance of X

Answer 1

Here, We have given two distributions

1) X~N(μ, σ2)

2) Z~N(0, 1)

From this description, X clearly follows a Normal distribution with mean μ and variance  σ2.

Therefore, the variance of X is σ2,

Var(X) = σ2.

From this description, Z clearly follows a standard Normal distribution with mean 0 and variance 1.

Therefore, the variance of Z is 1.

Var(Z) = 1

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