Exercise 7-3 (30 minutes)
a. Cash Flows from Operations Computation:
Net income.
Add (deduct) items to convert to cash basis:
Depreciation, depletion, and amortization.
Deferred income taxes.
Amortization of bond discount.
Increase in accounts payable.
De

BSP2014
Tutorial 2
1. Check whether the given function can serve as the probability mass function(p.m.f.)
of a random variable:
i) f(x) =
x 2
, for x = 1, 2, 3, 4, 5
5
ii) f(x) =
x2
, for x = 0, 1, 2, 3, 4
30
2. A random variable X has the following proba

BSP2014
Tutorial 7
1. Consider a Markov chain with transition probability matrix having state 1, 2 and 3
0.6 0.2 0.2
P = 0.4 0.5 0.1
0.6 0 0.4
i) Draw the transition diagram.
ii) Find P (2), P (4)
iii) Find P ( X 1 1 | X 0 1) , P( X 2 1 | X 0 2) and P(

BSP2014
Tutorial 1
1) Let P(A)=0.4 and P(A B)=0.6
i) For what value of P ( B ) are A and B mutually exclusive?
ii) For what value of P ( B ) are A and B independent?
2) There are total of 400 Beta students registered in Financial Engineering for Cyberjaya

BSP2014
Tutorial 4
1) A lot containing 4 good components and 3 defective components. A sample of 3 is
taken with replacement from the lot for inspection. Find the expected value and variance
of the number of good components in this sample.
2) If X is a di

BSP2014
Tutorial 6
1) Determine the parameter set T, and the state space S for the following stochastic
processes:
i) Dam problem:
Water flows into the dam from outside sources, and keep for use when needed.
Input and output depend on uncertainty, with th

BSP2014
Tutorial 5.2
(Continuous Joint Distribution)
1. The joint pdf of a two-dimensional RV (X,Y) is given by
e ( x y )
f(x, y) =
0
x 0, y 0
elsewhere
a) Determine whether f(x,y) can serve as a joint pdf or not.
b) Find P(X>1)
c) Find P(Y<1/2)
d) Fin

BSP2014
Tutorial 3.1
1. If the probability that a fluorescent light has useful life of at least 800 hours is 0.9,
find the probability that among 20 such lights
i) Exactly 18 will have a useful life
ii) At least 15 will have a useful life
iii) At least 2

BSP2014
Tutorial 3.2
1. Suppose the reaction time X of a randomly selected individual to a certain stimulus has a
gamma distribution with =1 second and =2 seconds. Find
(i) P(3<X<5)
(ii) P(X>4)
2. In a certain city, the daily consumption of electric power

BSP2014
Tutorial 8
1. Incoming telephone calls to an operator are assumed to be a Poisson process with
parameter =5 per minute.
(a) Find the probability that time between 2 calls is more than 30 seconds.
(b) Find the probability that time between 2 calls