Assignment#4(Solution)
Q#4.5 We consider the joint distribution, let X be N 3 ( , ) with,
3
11 12 13 1 2 0
1 , and 21 22 23 2 5 0
4
32 33 0 0 2
31
(b) We know that the conditional distribution of X2 given that X1=x1 and X3=x3 is also
norm
Solution Assignment#3
Q#4.2
Consider
a
bivariate
1 0, 2 2,11 2, 22 1, and 12 0.5.
(a)
normal
population
with
Since we know the p-dimensional multivariate normal distribution is given as,
1
1
(1)
f (X)
exp x 1 x
1/2
p/2
2
(2 )
If we have p=2, than the
Assignment#1(Solution)
Q#2.1(c) To compute the sample means, sample variances, sample covariance and sample
correlation coefficient, we proceed as follow.
(i)
The sample mean for p variables is defined as.
1 n
x jk , k 1, 2,., p
n j 1
xk
Here n=10 and k
Assignment#5(Solution)
Q#4.20(b) Let X 1 , X 2 ,., X 20 be the random sample form of size n 20 from N6 ,
population. Than specify the distribution of B 19S B when,
1 0 0 0 0 0
B
0 0 1 0 0 0
We also know that n 1 S ~ Wishart( n1)
B 19S B22 ~ Wishart19 i