for independent variables, the covariance will be 0. thus:
you have E[X] and E[X^2], from which you can find Var(X).
Finding Var(X+3Y) means that you are a step away from finding the s.d. Do that!
I can't seem to get the same answer as the back for this question. Can someone show me how to properly do it?
Let X and Y be two independent random variables where E(X) = 4, E(X^2)= 20 and V(Y)= 21. Find:
(a) V (X + 3Y)
(b) the standard deviation of (X+ + 3Y)
The answers at the back are 193 and 13.9.
Well, you should have a textbook and/or classnotes with you. And you should have been given these concepts before you are made to work on the problems.
Anyways, the three turns to 9 because it is a well known property.
For a random variable X with finite variance:
[Note: a is a constant]
The mean of is a times the mean of the random variable X.
Look HERE and
go here for Covariance