6) Suppose, you have 50 independent p = 2 dimensional observations 11,..., 150 following multivariate normal...

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6) Suppose, you have 50 independent p = 2 dimensional observations 11,..., 150 following multivariate normal distribution, with mean , and variance-covariance matrix . has 1 in the diagonals and off-diagonal entries are p, where P <1. Write down the density of their average (i.e. the average of 1,250's). Also, suppose you have 100 independent p = 2 dimensional observations 100 following multivariate normal distribution, with mean, and variance covariance matrix . Similarly, y is the average of y's, i = 1, . . ., 10. 4 Also, 100 are independent of 1,250- Construct an estimator using , which has expectation -2. Then construct a test for - 2 = (1,1) vs 2 (1, 1). 6) Suppose, you have 50 independent p = 2 dimensional observations 11,..., 150 following multivariate normal distribution, with mean , and variance-covariance matrix . has 1 in the diagonals and off-diagonal entries are p, where P <1. Write down the density of their average (i.e. the average of 1,250's). Also, suppose you have 100 independent p = 2 dimensional observations 100 following multivariate normal distribution, with mean, and variance covariance matrix . Similarly, y is the average of y's, i = 1, . . ., 10. 4 Also, 100 are independent of 1,250- Construct an estimator using , which has expectation -2. Then construct a test for - 2 = (1,1) vs 2 (1, 1).