Question

X1,...,X81 ⇠ N(0,1) and Y1,...,Y81 ⇠ N(3,2 ). For each i, Corr(Xi,Yi)= 1/2. Let Zi =...

X1,...,X81 ⇠ N(0,1) and Y1,...,Y81 ⇠ N(3,2 ). For each i, Corr(Xi,Yi)= 1/2. Let Zi = Xi + Yi.
1. Compute Var(Zi).
2. Approximate P [ Zi > 243]. (Explain your answer.)

Math   Statistics-And-Probability   
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Answer #1

Var(Zi) = 4.4142

And

P(Zi> 243) = 0 because for high value of z score, probability is zero.

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