1. assume y=1+x+u, where x, y, and u=v+x are random variables, v is independent of x; e(v)=0, var(v)=1, e(x)=1, and var(x)=2.

Var(u|X=1) = 1

Var(Y|X=1) = 1

Var(u|X) = 3

Var(Y|X) = 9

Step-by-step explanation:

First, we need to identify the properties of the variance, so:

1. Var(a) = 0 , if a is constant

2. ,  Where a is constant and X is a random variable

3. , Where a and b are constants and X is a random variable.

4. , Where X and Y are random variables and are independents.

Then, if Y=1+X+u, where X, Y, and u=v+X are random variables, v is independent of X; E(v)=0, Var(v)=1, E(X)=1, and Var(X)=2, the variance of the following cases are calculated as:

Var(u|X=1) = Var( v + X | X = 1) = Var( v + 1 )    

                 = Var(v) + Var(1)                            

                  = 1 + 0 = 1

Var(Y|X=1) = Var( 1 + X + u | X = 1 )

                 = Var (1 + X + v + X|X=1)

                 = Var(1 + 1 + v + 1)                      

                 = Var(3) + Var(v)                      

                 = 0 + 1 = 1

Var(u|X) = Var ( v + X | X)

             = Var ( v + X)

             = Var(v) + Var(X)

             =  1 + 2  = 3

Var(Y|X) = Var ( 1 + X + u | X)

             = Var ( 1 + X + v + X | X)

             = Var ( 1 + 2X + v)

             = Var(1) + Var(2X) + Var(v)

             = 0 + 4*2 + 1 = 8 + 1 = 9

it is b)

hope this : )

step-by-step explanation:

answer: if you weigh 60 pounds on earth, on the moon you will weigh about 10 pounds. if you weigh 120 pounds on earth, you will weigh about 20 pounds on the moon. since weight is caused by the mass of two objects that are near each other, the bigger the objects, the more the force of gravity.

step-by-step explanation: if you weigh 60 pounds on earth, on the moon you will weigh about 10 pounds. if you weigh 120 pounds on earth, you will weigh about 20 pounds on the moon. since weight is caused by the mass of two objects that are near each other, the bigger the objects, the more the force of gravity.