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8. Do not use computer. Given 2 [1 1 1] 1 Y = Y ~N3 -3 1 32 Y3 2 2 a) Find the

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8. Do not use computer. Given 2 [1 1 1] 1 Y = Y ~N3 -3 1 32 Y3 2 2 a) Find the probability P(Y < 3). b) Find the probability P(Y < 3|Y = 2). 2 STAT3600 c) Find the distribution of 1 X = [1-1 11] Y Hence, find the probability P(X < 3). d) Find a 2 1 vector, a, such that Y and Y - a' are independent.

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