Combinatorics and Intuitive
The simplest probabilistic scenario is perhaps one where the set of possible
outcomes is nite and these outcomes are all equally likely. A subset of the
set of possible outcomes is called an event. Computi
3. A computer program contains 6000 lines of code. This program is interpreted over a cloud
that contains two computers. On Computer 1, the program is indirectly execurted at a rate
of 300 lines per second. On Computer 2, the same program is interpreted a
R ANDOM S IGNALS AND S YSTEMS
TR 9:35 am 10:50 am
T 5:30 pm 6:40 pm
Dr. Jean-Francois Chamberland
MATH 308, junior or senior classication
1. Chapter 11: Multiple Continuous Random Variables.
2. Chapter 12: Convergence, Sequences and Limit Theorems.
1. Find the PDF of the continuous random variable X associated with the transform (moment
1. Chapter 9: Functions and Derived Distributions.
2. Chapter 10: Expectations and Bounds.
1. Consider the following two-sided exponential PDF
fX (x) =
x , x < 0
where and p are scalars with > 0 a
1. Chapter 8: Continuous Random Variables.
1. Let X be a random variable with probability density function
c 1 x2
1 < x < 1
f (x) =
(a) What is the value of c?
(b) What is the cumulative distribution
1. Two fair dice are rolled. Find the joint probability mass function of X and Y when
(a) X is the largest value obtained on any die and Y is the sum of the values;
(b) X is the value on the rst die and Y is the larger of the two va
1. A total of 4 buses carrying 148 students from the same school arrives at a football stadium.
The buses carry, respectively, 40, 33, 25, and 50 students. One of the students is randomly
selected. Let X denote the number of student
1. Chapter 5: Discrete Random Variables.
1. A well-shued 52-card deck is dealt to 4 players. Find the probability that each of the players
gets an ace.
2. There are 3 coins in a box. One is a two-headed coin; ano
1. Chapter 4: Conditional Probability
1. An urn contains 6 white and 9 black balls. If 4 balls are to be randomly selected without
replacement, what is the probability that the rst 2 selected are white and the la
1. Chapter 3: Basic Concepts of Probability
1. A die is rolled continually until a 6 appears, at which point the experiment stops. What is
the sample space of this experiment?
Let En denote the event that n rolls