Afire 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)

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-)Var(x) = 57

(1-)76 = 57

= 0.25

= 0.5

Var(y|x = 25) = (1-)Var(y)

                    = (1-)32

                    = 0.75×32 = 24

Var(y|x = 25)  = 24

intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction

step-by-step explanation:

required vector is consists of the two componentsvx= 2+4=6 units   and vy= 1 unit and vx ⊥ vywe will use pythagorian theorem to find intensity of the vector vv∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 unitsthe angle ∡α between vector and east direction we wil find with tanαtanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°

hope this