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What is 'n' in Central Limit Theorem

Created 2 years ago
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Maniteja
@Maniteja
Maniteja
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In lecture FDS #120,

What exactly is n representing in the CLT. Is it

--> Sample size of each sample (i.e. No. of elements in each sample) or

--> Total No. of samples of size , say 'm', drawn from a population.


This is my understanding. Please tell me if Iam wrong

We have population of size N with μ,σ as mean and SD.

Now if we create 'n' samples from the population of some size, say 'm', and

Define a RV Y : { Y: Xi_bar for all Xi E Rxi} and calculate the mean of each sample (X1bar, X2_bar, ... Xnbar) and plot all those values of yi=Xibar. This will follow a normal distribution with mean μ, E[Xbar] = μ; Var(X_bar) = σ^2/n

Also, In other words

instead of plotting means of each sample if we plot summation of values of all elements in a sample Xi and plot the distribution. It will follow N(nμ, σ sqrt(n) ) as n--> infinity. This is what CLT says.

No where it was mentioned what should be the sample size of each sample.


But in the same lecture, for the excercise part "to plot empirical distribution of sum of n iid samples from distribution D", 'n' was decribed as no. of values in each sample.

Please give some clarity on this. Thank you

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