Homework Set 2
1. Replace the set expression A B C with one using intersections and
complements. Replace the set expression A B C with one using unions and
2. Give the size of each set and also whether it is discrete or continuous.
Homework Set 7 SEE PROBLEM 5
1. A nonstationary (exponential, unstable in system terns) random process is defined
as X [n] a n U [n], where 0 < a < 1 where U[n] is WGN with variance U .
a. Find the mean and covariance sequences of X[n].
b. Transform the
Homework Set 8
1. A Bernoulli random process Xn for n consists of independent random
variables with each random variable taking on the values +1 and 1 with probabilities
p and 1 p, respectively.
a. Is this random process WSS?
Hint a: Is the process indepe
Homework Set 1
1. A fair coin is tossed. Identify the random experiment, the set of outcomes, and the
probabilities of each possible outcome.
2. Determine whether the following experiments have discrete or continuous
Homework Set 5
1. For the discrete random variable with PMF
p X [k ]
k 0, 1, ., 9
Find the expected value of X.
Hint 1: See notes, p. 173.
Hint 2: The answer is 4.5.
2. A coin is tossed with the probability of heads being 2/3. A head is mapp
Homework Set 4
1. Consider a random experiment for which S si : si 3, 2, 1, 0, 1, 2, 3 and the
outcomes are equally-likely. If a random variable is defined as X si si , find SX and the
Hint 1: Remember that you must convey all the probabili
Homework Set 6
1. Describe a random process that you are likely to encounter in the following
a. listening to the daily weather forecast
b. paying the monthly telephone bill
c. leaving for work in the morning (16.1)
Hint a: There are l