Suppose a particular state allows individuals filing tax returns to itemize deductions only if the total of all item- ized deductions is at least $5000. Let X (in 1000s of dol- lars) be the total of itemized deductions on a randomly chosen form. Assume that X has the pdf Sk/x k/x" x5 fix;

a) = { otherwise

a. Find the value of k. What restriction on a is necessary?

b. What is the cdf of X?

c. What is the expected total deduction on a randomly chosen form? What restriction on a is necessary for E(X) to be finite?

d. Show that In(X/5) has an exponential distribution with parameter a -1.