(Solved): An insurance company offers its policyholders a number of different payment options. For a randoml ...

An insurance company offers its policyholders a number of different payment options. For a randomly selected policyholder, let X = number of months between successive payments. The cdf is as follows:

PLEASE SHOW THE WORK AND EXPLAIN (Please DO NOT USE EXCEL, no shortcuts, etc.). Need to understand how to solve the problem.

3. An insurance company offers its policyholders a number of different payment options. For a randomly selected policyholder, let \( \mathrm{X}= \) number of months between successive payments. The cdf is as follows: \( \mathrm{F}(\mathrm{x})=\left\{\begin{array}{ll}0 & \mathrm{x}<1 \\ 0.3 & 1 \leq \mathrm{x}<3 \\ 0.4 & 3 \leq \mathrm{x}<4 \\ 0.45 & 4 \leq \mathrm{x}<6 \\ 0.6 & 6 \leq \mathrm{x}<12 \\ 1 & 12 \leq \mathrm{x}\end{array}\right. \) A) Compute \( \mathrm{P}(3 \leq \mathrm{X} \leq 6) \) ? (10 pts) B) Compute the expected optional payment? (10 pts)