Thread: Calculating Variance

The number of new houses being built depends on the 20 year mortgage rates offered by local banks. Let X be the random variable denoting the average 20 year mortgage rate measured in percentage points for a specific month. Assume that the expected value for X is 8.75 percentage points with a variance of 0.50. Define the random variable Y to be the number of new houses being built in a specific month. If Y = 85 - 2X, what is the variance of the random variable Y?

I am confused about how to calculate this?

It seems that there are three ways to calculate this, with the notes given to me.

Variance
X=Random Variable c=Constant
V(c)=0
V(X+c)=V(X)
V(cX)=C^2V(X)

I've been thinking of ways to solve this, but i keep on thinking it is only 85 since V(X+c)=V(X)

Originally Posted by deuscypher

The number of new houses being built depends on the 20 year mortgage rates offered by local banks. Let X be the random variable denoting the average 20 year mortgage rate measured in percentage points for a specific month. Assume that the expected value for X is 8.75 percentage points with a variance of 0.50. Define the random variable Y to be the number of new houses being built in a specific month. If Y = 85 - 2X, what is the variance of the random variable Y?

I am confused about how to calculate this?

It seems that there are three ways to calculate this, with the notes given to me.

Variance
X=Random Variable c=Constant
V(c)=0
V(X+c)=V(X)
V(cX)=C^2V(X)

I've been thinking of ways to solve this, but i keep on thinking it is only 85 since V(X+c)=V(X)

Var(aX + b) = a^2 Var(X).

In your case a = -2 and b = 85.