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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)

Respuesta :

Answer:

Var(y|x = 25)  = 24

Step-by-step explanation:

E(x)= 40    E(y) = 30

Var(x) = 76     Var(y) = 32

Var(x|y=28.5) = 57

(1-[tex]\rho^{2}[/tex])Var(x) = 57

(1-[tex]\rho^{2}[/tex])76 = 57

[tex]\rho^{2}[/tex] = 0.25

[tex]\rho[/tex] = 0.5

Var(y|x = 25) = (1-[tex]\rho^{2}[/tex])Var(y)

                    = (1-[tex]\0.5^{2}[/tex])32

                    = 0.75×32 = 24

Var(y|x = 25)  = 24

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