# Thread: Expected values and Variances

1. ## Expected values and Variances

Question 1:
Let where Xi's be i.i.d. Normal with mean 10 and variance 4 for i=1,2,...,16 and Yj's be i.i.d. Normal with mean 15 and variance 12 for j=1,2,...,10 and Ix & Yj are independent for all i & j. What is the value of E[W] and Var(W)?

Question 2:
Let Y= where Xi's be i.i.d. Normal with mean 10 and variance 4 for i=1,2,...,32. What is the value of E[Y] and Var(Y)?

Two very similar problems, but I'm lost. The rest of the homework is spelled out very carefully with hints, and these two are just on their own. I don't even know where to begin.

2. Hello,

First look here : Chi-square distribution - Wikipedia, the free encyclopedia
Your normal rv's are all subtracted by their mean, so $X_i-10$ and $Y_i-15$ are actually normal distributions with mean 0.
In order to make them standard normal distributions, recall that $\frac{X_i-\mu}{\sigma}$ follows a N(0,1).

Then look here : F-distribution - Wikipedia, the free encyclopedia

which will give you the results you're looking for.

3. Thanks. That is just what I needed.