ECE 552
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
complements.
2. Give the size of each set and also whether it is discrete or continuous.
a.
Homework Set 7 SEE PROBLEM 5
1. A nonstationary (exponential, unstable in system terns) random process is defined
2
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
ECE 552
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
outcomes:
a.
b.
c.
d.
e.
Throw
ECE 552
Homework Set 5
1. For the discrete random variable with PMF
p X [k ]
1
10
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
ECE 552
Homework Set 4
1. Consider a random experiment for which S si : si 3, 2, 1, 0, 1, 2, 3 and the
2
outcomes are equally-likely. If a random variable is defined as X si si , find SX and the
PMF.
Hint 1: Remember that you must convey all the probabili
ECE 552
Homework Set 6
1. Describe a random process that you are likely to encounter in the following
situations:
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