Y is the present-value random variable of an annuity that pays 1 at the beginning of each year that (x) survives.
You are given:
(i) E(Y) @ delta = 10
(ii) E(Y) @ 2delta = 6.
(iii) i = 1/24

Calculate the variance of Y.


The equation for the Var(Y) to use is 1/d2 * [(^2)A_x – A_x^2]
(Excuse the notation the 2's are raised and the x's are subscripts)
I got 1/d^2 to be 625 and I thought (i) was saying that A_x = 10 and (ii) that (^2)A_x = 6, but plugging these values in doesn’t return the right answer. Does anyone know what I’m doing wrong? Thanks!

Hey,
He gave us the formula 1=d(a_doubledot x)+Ax
Thats how we get Ax.

the 10 is equal to the a_doubledot x

So when I work that out, I get Ax=.6, but I don't know how to get the other part of that. I got the 625 to though.

Let me know if you get it.

To get the other part, try doubling the i, when I work it out, I get 111.53.

Close, any thoughts?

Ohh thanks for the help I got the last part!

delta = ln(1 + 1/24) = .040822
So 2delta = .081644 = ln(1 + i) , so i = .085069 and d = .0784
And 2A_x = 1 - d*6 = .5296
Andd then you get 106 when you plug it in
Thanks again!