A size 2 sample will be selected without replacement of a population X with values (2 , 4, 6). Let X 1 and X 2 be the values of the first and second extraction, respectively. (a) Determine the joint...

A size 2 sample will be selected without replacement of a population X

with values (2 , 4, 6). Let X₁
and X₂
be the values of the first and second extraction,

respectively.

(a) Determine the joint distribution of X₁
and X₂

(b) Determine the distribution of the sample mean X = (X₁+ X₂)/2.