# Describe the approximating normal random variable...

• Nov 13th 2009, 06:29 AM
AMK
Describe the approximating normal random variable...
Hey everyone, I feel like I should be getting this but I'm just not (Wondering)

Let X1, X2, .... , X60 be independent discrete random variables with mass function fX(x) = x/15, x=1,2,3,4,5

a) Let Xbar = (X1+X2+...+X60)/60 Describe the approximating normal random variable.
• Nov 13th 2009, 06:42 AM
theodds
Calculuate $E X_i$ and $\mbox{Var} X_i$, then $E\bar{X}$ and $\mbox{Var} \bar{X}$, and CLT that sucker. You find $E X_i$ and $\mbox{Var} X_i$ using the usual methods, then use those results and the rules for the expectation of sums and variance of sums under independence to get what you need for the sample mean (or you might just have memorized by this point that, if $\mu$ is the mean of the iid random variables, and $\sigma ^2$ is the variance, $E\bar{X} = \mu$ and $\mbox{Var}\bar{X} = \frac{\sigma ^2}{n}$, which is enough to fully define a univariate normal distribution).