Meet the t-distribution

- Let's look at a very useful family of distributions.…It's called the t-Distribution.…Now we've looked at the central limit theroem.…It's powerful, but it's limited in the real world.…Why is that?…The central limit theorem depends on population…parameters to calculate sampling distribution parameters.…In practice we rarely know enough about a population…to know its parameters.…You could argue that if we knew enough to know…a populations parameters…we wouldn't have to gather any data.…

So we don't know the population.…And that's why we use x bar and s to estimate mu and sigma.…The sampling distribution that we typically work with…follows a family of distributions called the t-distribution…and the members of this family…approximate a normal distribution.…How close a t-distribution comes to a normal distribution…depends on the sample size.…As far as its parameters are concerned…it's like the standard normal distribution.…

Mu equals zero and sigma equals one.…As for it's shape, the probability density function…is symmetric.…