p_40 = 0.9972 A_41 - A_40 = 0.00822^2A_41 -^2A_40 = 0.00433 Z is the present val
ID: 3179612 • Letter: P
Question
p_40 = 0.9972 A_41 - A_40 = 0.00822^2A_41 -^2A_40 = 0.00433 Z is the present value random variable for this insurance. Calculate Var (Z). Luke, a nonactuary, estimates the actuarial present value for a continuous whole life policy with a benefit of 100,000 on (30) by calculating the present value of 100,000 paid at the expected time of death. You may assume (30) is subject to a constant force of mortality, mu (x) = 0.05, and the force of interest is delta = 0.08. Determine the absolute value of the error of Luke's estimate.Explanation / Answer
GIVEN Sxx= 913.06 Syy= 2578.34 Sxy= 1327.89 x_bar= 15.23 y_bar= 28.94 a) correlation: r=sqrt(R-sq) r=Sxy/SQRT(Sxx*Syy) r= =B4/SQRT(B2*B3) b) X & Y RVs are positively correlated c) Error variance: R-sq= r^2 =B12^2 SStotal= Syy = =B3 SSR=SStotal * R-sq =B18*B17 SSE=Sstotal- SSR =B18-B19 Variance = SSE/n =B20/40 d) we need to 1st find point estimate and std error for alpha & beta = Sxy/Sxx= =B4/B2 = y_bar- *x_bar= =B6-B24*B5 Std error SE() = SQRT(MSE/Sxx) MSE=SSE/(n-2) = =B20/(40-2) SE() = SQRT(MSE/Sxx)= =SQRT(B29/B2) SE()= =SQRT(B29*(1/40+B5^2/B2)) t= =T.INV.2T(0.1,39) Upper CI for alpha= =B25-B33*B32 Lower CI for beta= =B24-B33*B30 f) p-value for hypothesis= =T.DIST.2T(B25/B32,39) Reject H0 and say alpha is significant g) p-value for hypothesis= =T.DIST.2T(B24/B30,39) Reject H0 and say beta is significant
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