a) Let X₁, X2, X3,..., X be a random sample of size n from population X. Suppose that X~N(0, 1) and Y= Σ=₁Xi-√√n. √n iii) Show using the moment generating function technique that Y is a standard normal random variable. iv) What is the probability that Y² is between 0.02 and 5.02?

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a)
Let X₁, X2, X3,..., Xn be a random sample of size n from population X. Suppose that X~N(0,1)
Σ1 Xi
and Y=
O√n.
√n
iii) Show using the moment generating function technique that Y is a standard normal random
variable.
iv) What is the probability that Y2 is between 0.02 and 5.02?
Transcribed Image Text:a) Let X₁, X2, X3,..., Xn be a random sample of size n from population X. Suppose that X~N(0,1) Σ1 Xi and Y= O√n. √n iii) Show using the moment generating function technique that Y is a standard normal random variable. iv) What is the probability that Y2 is between 0.02 and 5.02?
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