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9 Sep 2020
{(-1,0). (1,0), (0, –1), (0, 1)}. Show that Let X = (X1, X2) be uniform 1. on a) X1 and X2 are uncorrelated, but not independent b) X1-X2, and X1 + X2 are independent 2. Let Z1, Z2 be RV' with correlation coefficient between them. Further, let expectation of Z1, Z2 be 1 and -1, and variances 1, and 4, respectively. We define X := Z¡ – Z2 +1 and Y:= 3Z1 + 2Z2- 2. Find: a) Variance of X and Y b) Covariance and correlation coefficient of X and Y
{(-1,0). (1,0), (0, –1), (0, 1)}. Show that Let X = (X1, X2) be uniform 1. on a) X1 and X2 are uncorrelated, but not independent b) X1-X2, and X1 + X2 are independent 2. Let Z1, Z2 be RV' with correlation coefficient between them. Further, let expectation of Z1, Z2 be 1 and -1, and variances 1, and 4, respectively. We define X := Z¡ – Z2 +1 and Y:= 3Z1 + 2Z2- 2. Find: a) Variance of X and Y b) Covariance and correlation coefficient of X and Y
30 Jan 2023
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