Question

Prove the Following: Where a and b are constants.

a). Σ(?−?̅)=0

b). Var( a + bX) = b²Var(X)

Answer 1

a). We have to prove that  

, where a and b are constants.

Now, taking the left-hand side equation and proceeding:

Now, if we take summation inside the bracket, we get:

, is a constant term so, summation will change into

, there is the total number of observations

  

Hence,   Proved.

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NOTE:  

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b.)   

Taking the left-hand side equation and proceeding:

we can write it as:

  

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NOTE:

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NOTE:

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  proved.