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How do you use moment generating functions to show that [Xbar - mu / (sigma/sqrt(n))] follows...

How do you use moment generating functions to show that [Xbar - mu / (sigma/sqrt(n))] follows N(0,1)?

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Answer #1

By using the concept of Effect of Change of origin and scale on MGF.

E(Z)= 0 and V(Z)= 1 i.e mean and variance of a standard deviation are 0 and 1 respectively.

So that's how I can use MGF to show that Xbar - mu / (sigma/sqrt(n))] follows N(0,1)

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