i) Show that the standard score of the sample mean X, is equal to Y. ii) Show that the mean and variance of the random variable Y are 0 and 1, respectively. iii) Show using the moment generating function technique that Y is a standard normal random variable. ind What in 5033

MATLAB: An Introduction with Applications
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a)
QUESTION 1
Let X₁, X2, X3,..., X₁, be a random sample of size n from population X. Suppose that X~N(0, 1)
ΣΤ1
√n
-√
and Y =
i) Show that the standard score of the sample mean X, is equal to Y.
ii) Show that the mean and variance of the random variable Y are 0 and 1, respectively.
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) QUESTION 1 Let X₁, X2, X3,..., X₁, be a random sample of size n from population X. Suppose that X~N(0, 1) ΣΤ1 √n -√ and Y = i) Show that the standard score of the sample mean X, is equal to Y. ii) Show that the mean and variance of the random variable Y are 0 and 1, respectively. 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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