Suppose a particular state allows individuals filing tax returns to itemize deductions only if the total of all itemized deductions is at least $5000. Let X (in 1000s of dollars) be the total of itemized deductions on a randomly chosen form. Assume that X has the pdf f(x;a) = { k/xa x ≥ 5
0 otherwise
a. Find the value of k. What restriction on α is necessary?
b. What is the cdf of X?
c. What is the expected total deduction on a randomly chosen form? What restriction on α is necessary for E(X) to be finite?
d. Show that ln(X/5) has an exponential distribution with parameter α–1.