Suppose that X, Y, and Z are random variables with X ~ Bin(16, 1/4), Y ~ Geom(1/2), and Z ~ Poisson(5). Supposefurther that X and Z are independent but that X and Y are not independent. Match up the following quantities.E(4Y – 27)Drag answer here23E(Y² + Z²)Cannot be determinedDrag answer hereVar(2X + Y)36Drag answer here-2Var(X – Z)Drag answer hereVar(X + 2Z)Drag answer here

Answered: Image /qna-images/answer/cb2142eb-45e4-4a61-81d3-d5eb696c3513.jpg

Answered: Suppose that X,Y , and Z are random…

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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4. Suppose we have random variables W and Q, and we know Var(W) = 25, Var(Q) = 10, and Cov(W, Q) = 2. Now, let A = 2W + 4Q. What is Var(A)?
2. Let X and Y be random variables, and let a and b be constants. (a) Starting from the definition of covariance, show that Cov(aX,Y) = a Cov(X,Y). You may find it helpful to remember that if EX = µx, then EaX = aux. (b) Show that Cov(X + b, Y) = Cov(X,Y). Now let X, Y, Z be independent random variables with common variance o?. (c) Find the value of Corr(2X – 3Y + 4, 2Y – Z – 1). You may use any facts about covariance from - the notes, including those from parts (a) and (b) of this question, provided you state them clearly.
Suppose that X, Y, and Z are random variables with X - Bin(16, 1/4), Y ~ Geom(1/2), and Z ~ Poisson(5). Suppose further that X and Z are independent but that X and Y are not independent. Match up the following quantities. E(4Y – 2Z) Drag answer here 23 Var(2X + Y) 8 Drag answer here Var(X – Z) -2 Drag answer here E(Y² + Z®) Cannot be determined Drag answer here 36 Var(X+ 2Z) Drag answer here
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I roll a die with 10 faces numbered 0-9 and obtain a score X. What is E(X)? In order to obtain a random number between 0 and 99 I roll the die twice obtaining scores X and Y, then set Z = 10X + Y (i.e., the first roll determines the "tens", the second roll the "ones"). Is it true to say that E(Z) = 10E(X) + E(Y)?
Suppose we choose arbitrarily a point from the square with corners at(2,1), (3,1), (2,2), and (3,2). The random variable A is the area of the trianglewith its corners at (2,1), (3,1), and the chosen point. Compute E[A].

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