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(a) Var(X + Y ) = Var(X)+ Var(Y) (b) Ε(XY) - (EX) (EYΥ) (c) E(X + Y ) = EX+ EY

(a) Var(X + Y ) = Var(X)+ Var(Y) (b) Ε(XY) - (EX) (EYΥ) (c) E(X + Y ) = EX+ EY

A First Course in Probability (10th Edition)
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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For each of the identities in (a)-(f), choose an appropriate description from the following three options. Briefly explain your answers. (i) this identity holds in general (for any random variables X and Y). |(ii) this identity does not hold in general, but it holds if X and Y are independent. (iii) this identity may not hold even if X and Y are independent. (a) Var(X + Y) = Var(X)+ Var(Y) (b) E(XY) = (EX)(EY) (c) E(X + Y) = EX+EY (d) Var(XY) = Var(X)· Var(Y). (e) E[(X – EX)Y] = 0 (Hint: first distribute the multiplication by Y and use the linear property of the expectation, keeping in mind that EX is a constant.)
Transcribed Image Text:For each of the identities in (a)-(f), choose an appropriate description from the following three options. Briefly explain your answers. (i) this identity holds in general (for any random variables X and Y). |(ii) this identity does not hold in general, but it holds if X and Y are independent. (iii) this identity may not hold even if X and Y are independent. (a) Var(X + Y) = Var(X)+ Var(Y) (b) E(XY) = (EX)(EY) (c) E(X + Y) = EX+EY (d) Var(XY) = Var(X)· Var(Y). (e) E[(X – EX)Y] = 0 (Hint: first distribute the multiplication by Y and use the linear property of the expectation, keeping in mind that EX is a constant.)
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