Final answer:
To calculate the single benefit premium for the whole life insurance, we need to find the variance of the present-value random variable Z. The value of b is 0.01/c.
Step-by-step explanation:
To calculate the single benefit premium for the whole life insurance, we need to find the variance of the present-value random variable Z. Given the information provided:
a. To find the variance of Z, we need to calculate the expected value of Z^2.
Variance(Z) = E[Z^2] - (E[Z])^2.
From the given information, we know δ = 0.05 and t = 20.
Plugging in these values, we get
Variance(Z) = (b^2 + b*c + c^2) - (b+c)^2
= (b^2 + bc + c^2) - (b^2 + 2bc + c^2) = -bc.
b. Since the variance of Z is equal to -0.01, we can solve the equation -bc = -0.01 to find the value of b.
Solving for b, we get b = 0.01/c.
Therefore, the single benefit premium for this insurance is equal to Variance(Z), which is -0.01, and the value of b is 0.01/c.