Given E(Z), find Var(Z)

tbl9301 · #1 $Old$ October 11th, 2009, 02:55 PM

For a whole life insurance payable at the moment of death, you are given that E[Z] = 0.25. Assume that the forces of interest and mortality are constant. Calculate Var(Z).

So I know Ax = E[Z] = mu / (mu + d) when mu(x) = mu and we're supposed to use this result to help us calculate this problem. But I'm not sure how that fits together. Does anyone know how to use this or any other way to find the Var(Z)?

Thank you!

TKHunny · #2 $Old$ October 14th, 2009, 06:22 PM

Quote:

Originally Posted by tbl9301 $View Post$

For a whole life insurance payable at the moment of death, you are given that E[Z] = 0.25. Assume that the forces of interest and mortality are constant. Calculate Var(Z).

So I know Ax = E[Z] = mu / (mu + d) when mu(x) = mu and we're supposed to use this result to help us calculate this problem. But I'm not sure how that fits together. Does anyone know how to use this or any other way to find the Var(Z)?

Thank you!

Why did you learn the First Moment without leaning the Second Moment?

First Moment: $\bar{A}_{x} = \frac{\mu}{\delta + \mu}$

Second Moment: $^{2}\bar{A}_{x} = \frac{\mu}{2\delta + \mu}$

What else do you need for the Variance?

Use the First Moment, and the given value of 1/4, to solve for $\delta$ . Something magic will happen.