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Math Help - Calculating Variance

  1. #1
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    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)
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  2. #2
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    Quote Originally Posted by deuscypher View Post
    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.
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