7 Y is the present value random variable for a special 3year

7 Y is the present value random variable for a special 3-year temporary life annuity-due orn (G), you are given that: [i] tn= (0.9)\', t20; iil K is the curtate-future lifetime random variable for (3); (x), you are given that: 1.00, 1.87, 2.72, K K=0; K=1; 2,3, .. [iii] Y={ calculate Var[Y].

Solution

E(Y) = .1*1 + .09*1.87 + .81*2.72 = 2.4715
E(Y^2) = .1*(1^2) + .09*(1.87^2) + .81*(2.72^2) = 6.407
Var(Y) = 6.407-(2.4715^2) = 0.299