Sep 26, 2017 term paper 2

# SUPPOSE WE GENERATE A RANDOM VARIABLE X IN THE FOLLOWING WAY. FIRST WE FLIP A FAIR COIN. IF THE…

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1.Suppose we generate a random variable X in the following way. First we flip a fair coin. If the coin is heads, take X to have a Unif(O,1) distribution. If the coin is tails, take X to have a Unif(3,4) distribution. (a) Find the mean of X. (b) Find the standard deviation of X.

2. Let FX,Y (x,y)= {1/3 (x + y), 0 otherwise. FindVar(2X – 3Y + 8).

3. Let the random variable?? denote an individual’s blood calcium level and the random variable?? denote his or her blood cholesterol level. The joint PDF is????,??(??,??) = {1/240, 8.5 ?? ,120 ?? 0,????h????????????. Derive the marginal PDF of??,E(??),V(??), Derive the marginal PDF of??,E(??),V(??), Derive E(????),Cov(??,??), and interpret the covariance between?? and??.

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