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) =