Let the population x obey the normal distribution n (μ, σ ^ 2), x1, X2,..., xn be a sample from the population, let u = n ^ (1 / 2) * (x ˉ - μ) / σ, then d (U) =? Ask for detailed explanation

Let the population x obey the normal distribution n (μ, σ ^ 2), x1, X2,..., xn be a sample from the population, let u = n ^ (1 / 2) * (x ˉ - μ) / σ, then d (U) =? Ask for detailed explanation

U=n^(1/2)*(xˉ-μ)/σ~N(0,1),
D(U)=1.