Quantitative Analysis : P1.T2.306 Calculate the mean and variance of sums of variable

[BawBawBaw]

Good evening David,

Regarding question P1.T2.306 , question 306.1, I have a problem to understand why we need to apply the formula Var(x+y) in order to calculate the variance. The model gives ri=a*F + square(1-a^2)*e. Why cannot we apply the formula for the var (ax+by) ?
Many thanks in advance for your reply.

 

[ShaktiRathore]

Hi
The formulas Var(x+y) and Var(aX+bY) are almost the same except u put a=b=1 in the latter formula to get Var(x+y). Its difgerence in the form only otherwise both are technically the same both are calculating sum of variances of two variables only difference being that one has a and b coefficients of variables as unity.
Latter formula is a more general version of the former one. You shall get the same result whethrr u try one or the other. When u apply Var(X+Y) version u take out square of coefficients for each variable while in Var(aX+bY) the coefficients are already out as squares attached to the variable,so it makes no difference.
Thanks

 

[BawBawBaw]

Many thanks for your help @ShaktiRathore , very helpful