Let X1 be a normal random variable with mean 2 and variance 3, and let X2...
Let X1 be a normal random variable with mean 2 and variance 3, and let X2 be a normal random variable with mean 1 and variance 4. Assume that X1 and X2 are independent. What is the distribution of the linear combination Y = 2X1 + 3X2?
Homework Answers
Ans:
Linear combination of X1 and X2 is also normally distributed with :
mean=E(Y)=2*E(X1)+3*E(X2)
=2*2+3*1
=7
Var(Y)=2^2*Var(X1)+3^2*Var(X2)
=4*3+9*4
=12+36=48
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