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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Two randon variables Z and W are defined as Z = X + aY and W X - aY, where X and Y are also randomn variables. Find 'a' such that Z and W are orthogonal.
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if x1,X2, .... , X, be a random sample from Bim( 1,6). Show that T = x is UMVUE
.Two random variables X and Y have the joint pdf, fx y(x, y) = Ae-2x+y), x, y 2 0 elsewhere
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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.
ample 8•10. A computer while calculating correlation coefficient between two variables X and Y from 25 pairs ofobservations obtained the following results. n = 25, ΣχΕ 125, Ex2= 650, "Ey = 100, Σy-460 ΣΧΥ-508 correctly Prove that the It was, however, discovered at the time of checking that two pairs of observations were copied They noere taken as (6, 14) and (8, 6) while the correct values were (R, 12) and (6, correct value of the correlation coefficient should be 2/3.
Q7. Let X; (i = 1,.,n) be a random sample from the N(u, o²) population with unknown parameters u and o?. Then we know that T, = E-1(X - X)²/(n – 1) is an unbiased estimator -xi-1 . Now consider two other estimators T, and T3 for o? where of a? and further, (n-1)T T2 = E(X – X)*/n and T3 = E(X – X)²/n + 1). %3D What is the variance of T,? Find out the variances and biases of T2 and T3 and thus obtain their m.s.e.'s. Show that among the three estimators T,, T2 and T3 the one with minimum m.s.e. is T3.
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)?

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