3. A) If X and Y are independent random variables with variances ovariance of the random variable Z = -2X + 4Y 3.B) Repeat part A) if X and Y are not independent in and σxy = 1.=5 and o= 3, find the

In question (a) X & Y are independent Variance of x =5 , Variance of Y=3 Z= - 2X + 4Y - 3 We…

Answered: 3. A) If X and Y are independent random…

A First Course in Probability (10th Edition)

10th Edition

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Author:Sheldon Ross

Publisher:Sheldon Ross

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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The prevalence of mild myopia in adults over the age of 40 is 25% in the us supposed 4 adults over 40 are randomly chosen. Let Y denote the number of adult with myopia out of 4 with the following pmf of y Given X=10y-5 find the variance of X A) 75.10 B) 0.751 C) 70.10 D) 8.666
If X is a random variable having the standard normaldistribution and Y = X2, show that cov(X, Y) = 0 eventhough X and Y are evidently not independent.
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We have the following information about the random variables X and Y: |x = 1, |y = −1.5 , ox = 0.25, c} = 1. o Calculate the variance of Z = 3X + 5Y, a) when the coefficient of correlation is p(X, Y) = 0.46: 0²77 34.15 Z b) when X and Y are independent random variables: 0²2 27.75 X
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B) Let X1,X2, .,Xn be a random sample from a N(u, o2) population with both parameters unknown. Consider the two estimators S2 and ô? for o? where S2 is the sample variance, i.e. s2 =E,(X, – X)² and ở² = 'E".,(X1 – X)². [X = =E-, X, is the sample mean]. %3D n-1 Li%3D1 [Hint: a2 (п-1)52 -~x~-1 which has mean (n-1) and variance 2(n-1)] i) Show that S2 is unbiased for o2. Find variance of S2. ii) Find the bias of 62 and the variance of ô2. iii) Show that Mean Square Error (MSE) of ô2 is smaller than MSE of S?. iv) Show that both S2 and ô? are consistent estimators for o?.
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3. A) If X and Y are independent random variables with variances o variance of the random variable Z = −2X + 4Y - 3. B) Repeat part A) if X and Y are not independent in and Oxy = 1. = 5 and o = 3, find the