Let F be the c.d.f. of a discrete distribution that has the memoryless property stated in Theorem

Question:

Let F be the c.d.f. of a discrete that has the memoryless property stated in Theorem 5.5.5. Define (x) = log[1− F(x − 1)] for x = 1, 2, . . ..
a. Show that, for all integers t, h > 0, 1− F(h − 1) = 1− F(t + h − 1)/1− F(t − 1).
b. Prove that (t + h) = (t) + (h) for all integers t, h > 0.
c. Prove that (t) = t(1) for every integer t > 0.
d. Prove that F must be the c.d.f. of a geometric Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...