|Population||One Simple Random
y1, y2, ... , yn
|All Simple Random Samples of size n|
|Associated Mean(s)||Population mean µ, also called E(Y), or the expected value of Y, or the expectation of Y.||Sample mean ȳ = (y1+ y2+ ... + yn)/n||1) Each sample has its own mean ȳ.
This allows us to define a random variable Ȳn.
The population for Ȳn
is all simple random samples from Y. The
value of Ȳn for
a particular simple random sample is the sample mean ȳ
for that sample.
2) Since it is a random variable, Ȳn also has a mean, E( Ȳn). Using the model assumptions for this particular example, it can be proved that E( Ȳn) = µ. In other words, Y and Ȳn have the same mean as random variables.
|Associated Distribution||Distribution of Y||None||Sampling Distribution (Distribution of Ȳn )|