Joint Life Insurance Policy
A couple buys a life insurance policy together. Let y denote the respective remaining lifetime
A couple buys a life insurance policy together. Let y denote the remaining life in the respective years of the spouses, from the moment of creation policies. x and y are jointly and evenly distributed the region: (x, y): {0 <x <25} {x ² / 25 <y <25} Calculate the variance (X | Y = 16)
Because they are jointly uniformly distributed, we know that f (x, y) = (1 / 25) * (1 / (25 – (x ^ 2) / 25)) = 1 / (625 – x ^ 2), for 0 So f (x | Y = 16) = f (x, 16) / Prob (Y = 16) = [1 / 500] / [int_ (0 a 5 * sqrt (16)) de 1 / 500] = 1.20 , 0 <x <20 (= 5 * sqrt (16)). So now it is a direct variance calculation with the probability density function. Another way to see it more intuitive is again the inverse relationship and express the domain of x versus y, then y = 16 figure it limited to a maximum of 20, and their distribution uniform, so X | Y = 16 is a uniform (0.20).
