Question: Suppose that X and Y are bivariate normal random variables such that E[X] = 12, V[X] = 5, E[Y] = 1, V[Y] = 9, and

Suppose that X and Y are bivariate normal random variables such that E[X] = 12, V[X] = 5, E[Y] = 1, V[Y] = 9, and = 0.6.

Answer the following questions about this distribution:

(a) What is P(X 9)?

(b) What are E[X | Y = 0] and V[X | Y = 0]?

(c) What is P(X > 13 | Y = 0)?

(d) What are E[X | Y = 6] and V[X | Y = 6]?

(e) What is P(X > 13 | Y = 6)?

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