2. Consider random variable X and Y with µx= 0; 0x= 3; Hy = 1; 0y= 4. Assume that X and Y have covariance Cov[X,Y] = -3.
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![d. Are X and Y independen
2. Consider random variable X and Y with µx = 0; 0x= 3; µy = 1; 0y= 4. Assume that X and Y have
covariance Cov[X,Y] = -3.
a. Determine the expected value of Z = 2X + 2Y
b. Determine the variance ofZ= 2X + 2Y.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2043cac3-b634-4b4b-a2e4-5f29c6bf8c89%2F3c93bd6f-6130-4ed0-816a-265ae71dce21%2F4fpol5_processed.jpeg&w=3840&q=75)
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- Let the random variable X be defined on the support set (1,2) with pdf fX(x) = (4/15)x3, Find the variance of X.Let X and Y be independent random variables with means x,y and variances o, oy. Find an expression for the correlation of XY and Y in terms of these means and variances.Let I be an indicator variable with p(I) = {p , I=1 } {1-p , I=0}. Show that the variance of I is p(1-p)
- 8. Let y be a normal random variable with a constant mean E(y) = 4, constant variance var(y.) = o², and a covariance cov(y, y;) = 0 for t# j. Consider the sample mean j = E %3D A. Show that the variance of the sample mean y is .Let X be a random variable distributed as a Normal with mean 0 and variance 2 (i.e., X ~ N(0, 2)). Let Y be a random variable distributed as a Normal with mean 2 and variance 3 (i.e.., Y ~ N(2, 3)). X and Y are independent. What is the distribution of 2X – 5Y ?ox² = 3, oy² = 5, oxy = 2, Z = 2Y - 4X – 2 a. Determine the variance of Z.
- In a large lot of manufactured items, 10% contain exactly one defect and 5% contain more than one defect. If ten items are randomly selected from this lot for sale, the repair cost total Y1 +3Y2, where Y1 denote the number among the ten having one defective and let Y2 denote the number with two or more defects. Find the expected value and variance of the repair cost. Assume that Cov(Y1, Y2) =-0.05.The profit for a new product is given by Z=3X- Y-5 . If X and Y are independent random variables with Ox=1 and Oy=V2. What is the variance of Z ?