Help with rules of variances
I'm working on a problem where you have a normally distributed population with a mean of 60 and variance of 130. The question is, if you were to take 3 individuals from this population and take their average, what would be the mean value and vari?
I know that the average would just be (60+60+60)/3 = 60, but what about variance? The variance for the total would be 130+130+130 = 390. Would the variance for the average be (1/3²)*390 = 43.3?
Re: Help with rules of variances
Hint: If you have all independent observations then Var[aX + bY] = a^2*Var[X] + b^2*Var[Y] for random variables X and Y and constants (non-random) a and b.