Sampling Distribution of Sample Means: Roll a Fair Die Once
Central Limit Theorem
Let be independent, identically distributed random variables with
Then
Normal()
and
Normal()
To see this, it helps to look at examples. See one such example below.
Example
Roll a fair die once. Let be the outcome. Repeat times to get a sample of size . Compute the sample mean, . Repeat (or simulate) this times and record each sample mean; plot the sample means in green along with the pdf for Normal() in blue.
In the demo below, move:
- slider n to adjust the sample size
- slider t to adjust the number of simulations
- slider c to adjust the scale of the simulated sample means