Let X be a sign random variable with the distribution: Let P(X= 1) = 0.5; P(X=-1)...

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Let X be a sign random variable with the distribution: Let P(X= 1) = 0.5; P(X=-1) = 0.5. X (i) := 1 · [X(i, 1),..., X (i, n)] for i = 1,2,3. The elements (i, j), 1 ≤ i ≤ 3,1 ≤ j ≤ n are i.i.d. with the same distribution as X. Let Y₁, Y2, Y3,... be an i.i.d. sequence of random variables with mean zero and variance 1. Let Y random vector. Answer the following: (Y₁,..., Yn) be a = (1) (a) What will be the distribution of Z₁ = - YTX(1) as n becomes large? (b) What will be the distribution of the vector [Z₁, Z2, Z3] T as n becomes large? Here Z₁ = =YTX(;). Let X be a sign random variable with the distribution: Let P(X= 1) = 0.5; P(X=-1) = 0.5. X (i) := 1 · [X(i, 1),..., X (i, n)] for i = 1,2,3. The elements (i, j), 1 ≤ i ≤ 3,1 ≤ j ≤ n are i.i.d. with the same distribution as X. Let Y₁, Y2, Y3,... be an i.i.d. sequence of random variables with mean zero and variance 1. Let Y random vector. Answer the following: (Y₁,..., Yn) be a = (1) (a) What will be the distribution of Z₁ = - YTX(1) as n becomes large? (b) What will be the distribution of the vector [Z₁, Z2, Z3] T as n becomes large? Here Z₁ = =YTX(;).

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