1) Suppose X is a discrete variable that has the following probability density function
a) Calculate the cumulative distribution function (the cdf, or F(X))
b) Find the expected value of X. Show your work.
c) Find the variance of X. Show your work.
2) Consider the joint pdf for made-up data on PARTY by GENDER. You may want to enter these into a spreadsheet for this exercise.
a) Find the marginal (i.e. the unconditional) distribution of PARTY.
b) Find the marginal (i.e. the unconditional) distribution of GENDER.
c) What is the conditional pdf: f GENDER|Democrat. That is, given that you are Democrat, what is
the probability that you are male? Female?
d) Given the answers to (b) and (c), does there appear to be a relationship between party and
gender? Explain your reasoning.
3) Suppose you have the following random sample of values of X
a) What is E(X) and Var(X)? Write out the calculation in each case. When calculating Var(X), use the unbiased sample estimator, i.e. divide by n-1 instead of n.
b) What is the expected value of Y=0.3X-2?
c) What is the variance of Y?
4) Suppose Var(X)=3 and Var(Y)=9 and Corr(X,Y) = -0.6.
a) What is Var(X+Y)?
b) What is Var(X-Y)?