b. Show the set of all possible observations (n1, n2, n3) with n = 3
Answer : all possible observations are : (3, 0, 0), (2, 1, 0), (2, 0, 1), (1, 2, 0), (1, 1, 1),
(1, 0, 2), (0, 3, 0), (0, 2, 1), (0, 1, 2), (0, 0, 3)
c. Suppose (
π
1
,
π
2
,
π
3
) = (0.25, 0.50, 0.25). Find the multinomial probability that
(n1, n2, n3) = (1, 2, 0)
Answer: Multinomial probability is :
P (n1, n2, n3) = (n!/n1!n2!n3!)
π
1
n1
π
2
n2
π
3
n3
=(3!/1!2!0!) (0.25)
1
(0.50)
2
(0.50)
0
=
3 (0.25) (0.25) = 0.1875
d. Refer to ( c ) what probability distribution does n1 alone have?. Specify the values
of the sample size index and parameter for that distribution.
Answer: Binomial for n = 3 trials, and parameter
π
= 0.25
1.7) In his autobiography “A sort of Life”, British author Graham Greene
described a period of severe mental depression during which he played Russian
Roulette. This “game” consists of putting a bullet in one of the six chambers of a