Exam 3, 3pm Thurs May 20 2010
ECSE2500, Engineering Probability, Spring 2010, Rensselaer Polytechnic Institute
Answering 100 of the 130 points is a complete exam. However you have to mark the questions
that you don't want graded with a big X across each one.
1. A transmitter is sending a signal to a receiver over a noisy channel, with probability
p=1/2. When there is no transmitted signal, the number of photons that the receiver
sees is a discrete uniform random variable in the range [0,2]. However, when there
is
a
transmitted signal, the number of photons that the receiver sees is a discrete uniform
random variable in the range [1,4]. X is the random variable for the number of photons
that the receiver sees.
1.
(5)
What is P[X=k] for k= 0, 1, 2, 3?
2.
(5)
What is P[signal presentX=k] for k= 0, 1, 2, 3?
3.
(5)
What is T, the threshhold value of k for which P[signal presentk] >= 1/2?
4.
(5)
Pretend that T=1. If you use the decision rule that a signal is present if X>=T,
then what is the probability that this rule gives the correct answer?
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document2. Students applying to RPI:
o
Pretend that there are 3,000,000 high school grads this year.
o
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '11
 Radke
 Probability, Rensselaer Polytechnic Institute, Cumulative distribution function, Discrete probability distribution

Click to edit the document details