Exercise 7-3 (30 minutes)
a. Cash Flows from Operations Computation:
Add (deduct) items to convert to cash basis:
Depreciation, depletion, and amortization.
Deferred income taxes.
Amortization of bond discount.
Increase in accounts payable.
1. Check whether the given function can serve as the probability mass function(p.m.f.)
of a random variable:
i) f(x) =
, for x = 1, 2, 3, 4, 5
ii) f(x) =
, for x = 0, 1, 2, 3, 4
2. A random variable X has the following proba
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(
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
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
1) Determine the parameter set T, and the state space S for the following stochastic
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
(Continuous Joint Distribution)
1. The joint pdf of a two-dimensional RV (X,Y) is given by
e ( x y )
f(x, y) =
x 0, y 0
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)
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
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
2. In a certain city, the daily consumption of electric power
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