QA Bank: Q2.1(vi)

Why its answer isn't C ?
since X and Y are Random Variables, therefore they can't be constants and statement is true only for constants.

 

C means Var (XY) is never equal to Var(X)Var(Y)
which is a wrong statement because there may be some X and Y for which this equality holds.

 

Then which reason should be stated in exam alongwith answer - this one or the one which is provided in book .

 

Whichever u like. But TBH, the reason given in the book doesn't seem right to me as well. Because if X and Y are RV then they can't be constants.

Also in part(viii) they've chosen option C, because X can't be constant according to them. So these two reasons are contradicting.

 

A random variable which takes only one value is referred to as a constant random variable or degenerate random variable. You can read this wiki article.

So, the reasoning for part vi is okay.

In part viii, we are trying to prove Var(-X) = -Var(X). Note variance of any RV is always non-negative. So this relation can never be true unless the RV is itself a constant. So, I agree that the solution can be better structured

 

1. i got for the vi ques.
2. & then answer to viii ques should be D (if we keep both answer's reasoning same) that 'its only true in exceptional circumstances eg if X is constant RV.