Question: LetXbe standard normal. Construct a random variableYas follows: Toss a fair coin. If the coin lands heads, letY=X. If the coin lands tails, letY=X. (a)

LetXbe standard normal. Construct a random variableYas follows:

  • Toss a fair coin.
  • If the coin lands heads, letY=X.
  • If the coin lands tails, letY=X.

(a) Find the cdf ofY.

(b) Find E(XY)by conditioning on the result of the toss.

(c) AreXandYuncorrelated?

(d) AreXandYindependent?

(e) Is the joint distribution ofXandYbivariate normal?

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