Let X₁, X₂, X3, ..., Xn be a random sample of size n from population X. Suppose that X~N(0, 1) and Y = Σ₁=1X₁-0√n. √n

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 6CR
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2.STATISTICAL INFERENCE
Question 1 a ii)

a)
Let X₁, X₂, X3, ..., Xn be a random sample of size n from population X. Suppose that X~N(0, 1)
Σ₁=1 Xi
and Y =
i=1:
√n
- 0√n.
ii) Show that the mean and variance of the random variable Y are 0 and 1, respectively.
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=1 Xi and Y = i=1: √n - 0√n. ii) Show that the mean and variance of the random variable Y are 0 and 1, respectively.
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