Here, X is the sample mean of X, ... ,Xp. ( a) Show that Σ(Χ, - X)" Σχ)-ηX? (b) Show that E(E X) = n(µ² + o²) [Hint: E(Y²) = Var(Y) + [E(Y)]².] (c) Show that E (nX²) = nµ² + o². [Hint: Apply the similar relation given in the previous hint]

Here, X is the sample mean of X, ... ,Xp. ( a) Show that Σ(Χ, - X)" Σχ)-ηX? (b) Show that E(E X) = n(µ² + o²) [Hint: E(Y²) = Var(Y) + [E(Y)]².] (c) Show that E (nX²) = nµ² + o². [Hint: Apply the similar relation given in the previous hint]

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

3. Let X₁, … , X_n" be a random sample from a distribution with mean μ and variance σ_2.

Here, X is the sample mean of X, ... ,Xp.
( a) Show that Σ(Χ, - X)" Σχ)-ηX?
(b) Show that E(E X) = n(µ² + o²) [Hint: E(Y²) = Var(Y) + [E(Y)]².]
(c) Show that E (nX²) = nµ² + o². [Hint: Apply the similar relation given in the previous hint]

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