Question

Let T1 and T2 be independent random variables with Var(T1) = 9 and Var(T2) = 3....

Let T1 and T2 be independent random variables with Var(T1) = 9 and Var(T2) = 3. Compute Var(T1 –T2).

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Answer #1

we have given Var(T1) = 9 and Var(T2) = 3.

Here we use the formula

Var(X - Y ) = var ( X ) - 2 Cov( X,Y ) + Var ( Y )       

Cov(X , Y)    means the covariance betweeen X andY

apply above formula we get

Var(T1 - T2 ) = var ( T1 ) - 2 Cov( T1 ,T2 ) + Var ( T2 )     

But we have given T1 and T2 are the Independent

Therefore we

Cov( T1 ,T2 ) = 0 ( This is the condtion for the Indepent random varaible )

We plug that value in formula so we get

Var(T1 - T2 ) = 9 - 2 * 0 + 3

Var(T1 - T2 ) = 9 - 0 + 3

Var(T1 - T2 ) = 9 + 3

Var(T1 - T2 ) = 9 + 3

Var(T1 - T2 ) = 12

So we get the Final answer as :-

Var(T1 - T2 ) = 12

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