Let Xi, i=1, ,10, be independent random variables

[TomJerry]

Let Xi, i=1,...,10, be independent random variables, each uniformly distributed over (0, 1). Calculate an approximation to P($$\sum$$X_i > 6)
Solution

E(x) = 1/2
and
Var(X) = 1/12

[How should is calulate the approxmiate ]

 

[statdad]

Remember what the central limit theorem says about approximating sampling distributions of means if i.i.d random variables: you can also use it to obtain the sampling distribution of the sum of i.i.d random variables.

 

[bpet]

Interestingly, Berry-Esseen gives $$p\approx 0.137 \pm 0.2$$ whereas the true error is closer to 0.002. Do any other theorems give more accurate error estimates?