The Central Limit Theorem States: If X is from a population with mean mu and var

Question

The Central Limit Theorem States: If X is from a population with mean mu and variance sigma squared , and your sample size is ____________ (Large, Linear, Small or Normal), then the distribution of ___________(sigma^2, x-bar, mu, s^2) is Normal with a mean of ____________(mu/sqrt(n), mu^2, (mu^2)/n, or mu) and variance of _________ (sigma/sqrt(n), sigma^2, (sigma^2)/n, or sigma), regardless of the underlying distribution of X.

Fill in the blanks with the proper word in parenthesis and please explain. Thank you!

Explanation / Answer

Central limit theorem says that for a large sample n(x_bar-mu) will follow normal distribution with mean 0 and variance sigma^2 regardless of whatever be the distribution of X but X's need to be identical and independent random variables. It is the form of weak convergence.

Now coming to answers

1-large

2-x-bar

3-mu

4-(sigma^2)/n

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