# Central limit theorom

1. Nov 3, 2006

### majin

just a query......... does anyone have a general definition of the central limit theorom. Ive been looking on the internet and all ive got is a whole lot of complex crap

P.S it would help if it was related to fisheries management

2. Nov 5, 2006

### marcmtlca

simply put: under certain regularity conditions (finiteness of mean and variance), given Y_i are independent and identically distributed random variables.

$$\frac{\sqrt{n}}{\sigma}(\frac{1}{n}\sum_{i=1}^{n}Y_i-\mu) \rightarrow N(0,1)$$

You can think of the $$Y_i$$ as fish that you are sampling from a population of fish who's mean age and variance you know. Then if you sample a large amount of fish. The average age of your sampled fish standardized as above will be approximately normal(0,1).

Last edited: Nov 5, 2006
3. Nov 6, 2006

### FunkyDwarf

the one we were taught is that sqrt(n)(X-u)/(s) - >N(0,1) if s>30 otherwise you gotta use the t distribution where s is the sample std deviation

4. Nov 6, 2006

### marcmtlca

ya so if your n is not large enough, the approximation is not comfortable enough to use the normal. thats fine.

5. Nov 6, 2006

### FunkyDwarf

yeh so as n->infinity the t distrubution tends to the normal