# independent random variables, averages, and more...

• August 2nd 2011, 08:28 PM
iamthemanyes
independent random variables, averages, and more...
Suppose X_1, X_2, ... , X_100 are independent random variables with common mean "mu" and variance "sigma squared." Let X be their average. What is the probability that
|X - "mu" | is greater than or equal to 0.25?

I can tell that this has something to do with either the weak law of large numbers or the central limit theorem, but something isn't clicking. Thanks!
• August 3rd 2011, 12:27 AM
Moo
Re: independent random variables, averages, and more...
Hello,

You won't be able to have the exact probability...
You can have an upper bound for the probability with Chebyshev's inequality.
And you can have an approximation thanks to the CLT.

In both cases, it would depend on $\sigma^2$, I guess that's what is missing.