Exercise 2. Let p = [0, 1] and let random variables X₁,..., Xn be i.i.d., such that P(X; = 1) = pand P(X₂ = 0) = 1-p for all i = {1,2,...,n}. Finally, let X be the average of the X₁.a) Determine E(X₂) and Var(X₂).b) Determine E(X) and Var (X).c) Show thatP(X = k/n) = (7) p² (1- (^)^(1-2)^-^.k p)"-Exercise 3. Let X be a random variable with mean µ and variance o². For a € R, consider theexpectation E((X -a)²).a) Write E((X-a)²) in terms of a, μ and o².b) For which value a is E((X - a)2) minimal?c) For the value a from part (b), what is E((X− a)²)?

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Exercise 2. Let p = [0, 1] and let random variables X₁,..., Xn be i.i.d., such that P(X₂ = 1) = p and P(X₂ = 0) = 1-p for all i = {1, 2,...,n}. Finally, let X be the average of the X₁. a) Determine E(X;) and Var(X₂). b) Determine E(X) and Var(X). c) Show that P(X = k/n) = (*)p² (1 − p)”-k,

Exercise 2. Let p = [0, 1] and let random variables X₁,..., Xn be i.i.d., such that P(X₂ = 1) = p and P(X₂ = 0) = 1-p for all i = {1, 2,...,n}. Finally, let X be the average of the X₁. a) Determine E(X;) and Var(X₂). b) Determine E(X) and Var(X). c) Show that P(X = k/n) = (*)p² (1 − p)”-k,

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter2: Equations And Inequalities

Section2.7: More On Inequalities

Problem 44E

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