MA3160a6 Markov Chain 1112B
1. Three white and three black balls are distributed in two urns in such a way that each contains three
balls. We say that the system is in state i , i = 0,1, 2,3 , if the
MA3160a5 Poisson Process 1112B
1.
Cars pass a certain street location according to a Poisson process with rate . A man who wants to
cross the street at that location waits until he can see that no car
MA3160a4 Distribution 1112B
1.
Let X and Y be independent Bernoulli random variables with parameter
1
. Show that X + Y and
2
X + Y are dependent though uncorrelated.
2.
3.
Let X 1 , X 2 be independen
MA3160a3 Random Vector 1112B
1. Express the distribution of the followings in terms of the distribution function FX of the random
variable X.
(a) X + = maxcfw_0, X .
(b)
(c)
X = mincfw_0, X .
X = X+ +
MA3160a2 Random Variable 1112B
1.
2.
3.
4.
3
. The process continues
5
until a player has won two more games than the other. The overall winner is the first player to have
won two more games than the
MA3160a1 Probability 1112B
1. Consider two events A and B such that P ( A) = 0.4 and P ( B ) = 0.7 . Determine the maximum and
minimum possible values of P ( A B ) and the conditions under which each
MA3160a7 1112B
1.
Queueing
Cars arrive at a petrol pump with exponential inter-arrival times having mean
1
minutes. The
2
1
minutes per car to supply petrol, the service times being
3
exponentially di
MA3160a5 Poisson Process 1112B
1. Cars pass a certain street location according to a Poisson process with rate . A man who wants to
cross the street at that location waits until he can see that no car
MA3160a4 Distribution 1112B
1.
Let X and Y be independent Bernoulli random variables with parameter
1
. Show that X + Y and
2
X + Y are dependent though uncorrelated.
Proof:
0
X
1
Probability
2
Consid
MA3160a3 Random Vectors 1112B
1. Express the distribution of the followings in terms of the distribution function FX of the random
variable X.
(a) X + = maxcfw_0, X .
(b) X = mincfw_0, X .
(c) X = X +
MA3160a2
1.
Random Variable 1112B
3
. The process continues
5
until a player has won two more games than the other. The overall winner is the first player to have
won two more games than the other.
(a
MA3160a1 Probability 1112B
1. Consider two events A and B such that P ( A) = 0.4 and P ( B ) = 0.7 . Determine the maximum and
minimum possible values of P ( A B ) and the conditions under which each
MA3160a7 Queueing 1112B
1.
Cars arrive at a petrol pump with exponential inter-arrival times having mean
1
minutes. The
2
1
minutes per car to supply petrol, the service times being
3
exponentially di
MA3160a6 Markov Chain 1112B
1. Three white and three black balls are distributed in two urns in such a way that each contains three
balls. We say that the system is in state i , i = 0,1, 2,3 , if the