Thread: Random Variables

We are discussing random variables in class, but have only discussed theoretical application, and I am lost as to how to figure out word problems. Here is one from my homework:

An insurance company writes a policy to the effect that an amount of money A must be paid if some event E occurs within a year. If the company estimates that E will occur within a year with probability p, what should it charge the customer in order that its expected profit will be 10 percent of A?

Originally Posted by lexietx

We are discussing random variables in class, but have only discussed theoretical application, and I am lost as to how to figure out word problems. Here is one from my homework:

An insurance company writes a policy to the effect that an amount of money A must be paid if some event E occurs within a year. If the company estimates that E will occur within a year with probability p, what should it charge the customer in order that its expected profit will be 10 percent of A?

The expected payout is . So if the insurance company charges the expected profit will be zero. For the expected profit to be the insurance company must therefore charge ..... ? (this is called a leading question, by the way).

They are just going to want to charge pA plus 1/10th of A? Wow, that just seemed way too uncomplicated

Originally Posted by lexietx

They are just going to want to charge pA plus 1/10th of A? Wow, that just seemed way too uncomplicated

A little too jumpy, there. You should have followed the lead, rather than think you were done.

Expected Income = I
Expected Payout = pA
Expected Profit: I - pA = A(0.10)

It helps if you prove it, demonstrate it, or let the notation tell you what it is. What it SEEMS is of very little importance. Make the notation say what is needed.

haha thanks