Suppose there is a population with 20 short people and 60 tall people. You randomly sample one person. If the sampled person is short, record X = 0 and then flip a coin. Then, if the coin comes up heads, record Y = 0; if the coin comes up tails, record Y = 1. If the sampled person is tall, record X =1 and Y = 0. (That is, if the person selected is tall, you do not flip a coin.)

• What is the joint p.m.f. of X and Y?
• What is the marginal p.m.f. of X?
• What is the conditional p.m.f. of Y given X = 0?
• What is the conditional p.m.f. of Y given X = 1?
• What is the conditional expectation function of Y given X?
• What is the covariance of Y and X?
• What is the (marginal) variance of X?
• What is the best linear predictor of Y given X?
• (1pt bonus) plot CEF and BLP using R.