I am a little confused over it as to, if my EPV is correct using my own expression (Attached) of the EPV, then why is the same expression giving me a wrong answer for the variance? Is my expression for the EPV not correct? I am just wondering, where I am going wrong? My solution is attached: Thanks for any help!! Question is as below: Examiner's Solution is:
In this question you have broken them in to term assurance and whole life so when you calculate the expected value so this expression will work because for the first 10 years when you add 0.75* whole + 0.25 * term assurance = 0.75+0.25 = 1 but when you talk about calculating the second moment so in the first 10 years it should for 1^2 but if you see you added 0.75^2 + 0.25^2 so it does not come equal to 1 so if you want to adopt your method so the formula for calculating the variance will be this one is T = terms assurance one is W = whole life var(W + T) = var (W) + Var(T) + 2 cov(W,T) var(W) = 0.75^2 * var(W) var(T) = 0.25^2 * var(T) cov(W,T) = E(WT) - E(W)*E(T) E(WT) = 0.75*0.25 * second moment of term assurance) E(W) = 0.75*expected value of whole life assurnace E(T) = 0.25*expected value of term assurnace
