Question

HELP!! WILL FAN AND MEDAL!!

Find the sampling distribution of sample means if all possible samples of size 2 are drawn with replacement from the following population

X -2 0 2
p(x) 0.2 0.6 0.2

Answer 1

All this asks is for you to find the population mean of sample means and the standard deviation of all sample means. The population mean of sample means is just the expected value of X.

\[\mu _{^{sample mean x}} = E(x) = \sum_{i=1}^{n}x_{i} P(x _{i})\]

The standard deviation of the mean (or standard error) is given by

\[\sigma _{mean} = \frac{ \sigma }{ \sqrt{n} }\]

Answer 2

thanks for your help!! :D