Suppose that X, Y, and Z are random variables with X~ Bin(7, 1/6), Y ~ Geom(1/2), andZ Poisson (6). Suppose further that X and Y are independent but that X and Z are notindependent. Match up the following quantities.Var(2X + Y)Drag answer hereVar(X + Y)Drag answer hereE(Y² – Z²)Drag answer hereE(-Y + Z)Drag answer hereVar(X + 2Z)Drag answer here4-36107/36Cannot be determined53/9

Given that X, Y and Z are random variables with X~Bin7,16Y~Geom12Z~Poisson6 X and Y are independent.…

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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Show that if X, Y are independent random variables, then Cov(X, Y ) = 0.
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)?
7. Complete the spreadsheet section below so that columns A through C are complete for numbers 1 to 100. (The value for a should be a random number generated by the formula in cell E1.) A B C D E 1 X x^2 x^2+a a =RANDBETWEEN(-10,10) 2 1 2
7) Suppose that X and Y are two independent measurements. We can treat these measurements as random variables, where X has the mean of 1 and standard deviation of 2, and Y has the mean of 2 and the standard deviation of 3. For the transformations below, find the mean, variance, and the standard deviation. a) X+Y b) X-Y c) 2X+Y d) X-2Y+1
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
Let (Ω, Pr) be a probability space, and let X and Y be two independent random variables that are positive and have non-zero variance. (a) Prove that X^2 and Y are independent. Note that by symmetry, it will also follow that Y^2 and X are independent. (b) Use the result from part (a) to show that the random variables W = X + Y and Z = XY are positively correlated (i.e. Cov(W, Z) > 0).
2. Let the independent random variables X1 and X2 have Bin(0.1,2) and Bin(0.5, 3), respectively. (a) Find P(X1 = 2 and X2 = 2). (b) Find P(X1 + X2 = 1). (c) Find E(X1 + X2). (d) Find Var(X1 + X2).
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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Suppose that X, Y, and Z are random variables with X Bin(7, 1/6), Y Geom(1/2), and Poisson(6). Suppose further that X and Y are independent but that X and Z are not independent. Match up the following quantities. Z ~ Var(2X + Y) ~ ~