Independent random variables X_{1} and X_{2} are combined according to the formula L = 3*X_{1} + 2*X_{2}. If X_{1} and X_{2} both have a variance of 2.0, what is the variance of L?

nitraiddQ 2020-11-22 Answered
Independent random variables X1andX2 are combined according to the formula L=3X1+2X2.
If X1andX2 both have a variance of 2.0, what is the variance of L?
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Expert Answer

Usamah Prosser
Answered 2020-11-23 Author has 86 answers
Step 1
X1andX2 are independent random variables.
V(X1)=V(X2)=2
COV(X1,X2)=0,asX1andX2 are independent random variables.
V(L)=V(3X1+2X2)=9V(X1)+4V(X2)+12COV(X1,X2)
=92+32
=132=26
V(L)=26
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