Let X be a standard normal random variable Another random variable is determined as follows We flip a fair coin (independent from X) In case of Heads, we let Y X In case of Tails, we let Y X (1) Is Y Normal Yes No Not enough information to determine (2) What is the Cov (X,Y) Cov (X,Y) (3) Are X and Y independent Yes No Not enough information to determine (4) Find P(X Y 0) P(X Y 0)

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Question: Let X be a standard normal random variable. Another random variable is determined as follows. We flip a fair coin (independent from X). In case

Let X be a standard normal random variable. Another random variable is determined as follows. We flip a fair coin (independent from X). In case of Heads, we let Y=X. In case of Tails, we let Y=X.

(1) Is Y Normal?

Yes
No
Not enough information to determine

(2) What is the Cov (X,Y)

Cov (X,Y) =

(3) Are X and Y independent?

Yes
No
Not enough information to determine

(4) Find P(X + Y 0)

P(X + Y 0) =

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