Thread: Mean/Var of RV of Averaged Random #s

1. Mean/Var of RV of Averaged Random #s

I'm trying to find the mean and variance of a random variable which is the average of 4 random numbers from a uniform distribution between 0 and 1. Anyone know how to go about finding this? Any help would be much appreciated.

Thanks!

2. $E(X_i)=1/2$ for all i

Thus $E(\bar X)=1/2$ even without independence

Likewise $V(X_i)=1/12$ for all i, that's ${(b-a)^2\over 12}$

So $V(\bar X)=V(X_i)/n={1\over 12n}={1\over 48}$ where we need independence here