Let

where X's be i.i.d. Normal with mean 10 and variance 4 for i=1,2,...,16 and Y's be i.i.d. Normal with mean 15 and variance 12 for j=1,2,...10 and X and Y are independent for all i and j. What is the value of E[W]?

Professor's answer:

My Question:

Why 120/64?

I always get 64/120.

Any help is greatly appreciated.