Bivariate or joint probability distributions

12
In particular, suppose X 1
, X 2
..... X n
form a random sample from a Normal
population with mean µ and variance σ 2 ,
2 2 2 2
µ = µ = µ = ..... = µ = µ and σ = σ = ..... = σ = σ .
1 2 3 n
1
∑
Y ~ N( a µ , a
2 σ
2 ).
i
∑
i
2
n
Further, suppose that a = a = a = ..... = a =
1 2 3
n
1
n
then Y = X + X + X
1 2
...
n
n
=
X
and X ~ N( µ , σ 2 ) .
n