2. For any r.v.'s X₁,..., Xn, set(a) Show thatnni=1Xi, and 5²nn(X − X)2.nnn5² = Σ(X₁ − X)² = ΣX² − n(X)².i=1i=1(b) If the r.v.'s have the common finite expectation µ, thennnΣ(Xi − µ)² = Σ(Xi − Ñ)² + n(Ñ − µ)² = n5² + n(Ñ − µ)².i=1i=1

Answered: 2. For any r.V. S X1,..., Χη, set (a)…

A First Course in Probability (10th Edition)

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Chapter1: Combinatorial Analysis

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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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Let X-(1,0,– 1,–/2)'. Then, ||X||=V2 %3D Select one: O True False امتحان نص Jump to...
Consider a (non)-symmetric random walk M = Xo +X1+X2+…+Xn where X;'s (i> 1) are independent and identical distributed, P(X; = 1) = p and P(X;=-1) =1–p and Xo = 0. Let Sn = eaS,-n Denote Fn= 0(X1,...,Xn). Find a such that (Sn)n20 is a (Fn)n20 - martingale.
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2. For any r.V. S X1,..., Χη, set (a) Show that η X x - Σxi, and 52 - Σ - x). = Σ(x η i=1 i=1 n n n52 = Σ(x − x) = Σx - n(X)2. - = i=1 i=1 (b) If the r.v.’s have the common finite expectation μ, then n n Σ(X; - μ)2 = Σ(x - X)2 + n(X - μ)2 = nā2 + n(X - μ). – i=1 i=1