Question

A fire in an apartment building results in a loss, x, to the owner and a loss, y, to the tenants. the variables x and y have a bivariate normal distribution with e(x) = 40, var(x) = 76, e(y) = 30, var(y) = 32, and var(x | y = 28.5) = 57. calculate var(y | x = 25). (a)

Answer 1

Var(y|x = 25) = 24

Explanation:

E(x)= 40 E(y) = 30

Var(x) = 76 Var(y) = 32

Var(x|y=28.5) = 57

(1-
`\rho^(2)`)Var(x) = 57

(1-
`\rho^(2)`)76 = 57

`\rho^(2)` = 0.25

`\rho` = 0.5

Var(y|x = 25) = (1-
`\rho^(2)`)Var(y)

= (1-
`\0.5^(2)`)32

= 0.75×32 = 24

Var(y|x = 25) = 24