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(ELEC2600)[2011](s)midterm~lzhangab^_24535.pdf
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The Hong Kong University of Science and Technology
Department of Electronic and Computer Engineering
ELEC 210: Probability and Random Processes in Electrical Engineering
2011 Spring Semester
Midterm Test
March 23, 2011

Name:
Student ID:
Instructions:

1.
This is an 80-minute test.


2.
You may use a non-programmable calculator.

3.
There are 2 sections:


a.
Section 1: 5 Multiple Choice Questions

b.
Section II: 4 Problems



4.
Try to attempt all questions.

5.
Answer each question in your answer booklet.

6.
The distribution of marks is shown in the table below:


Question Mark
Multi. Choice 20
1 20
2 20
3 20
4 20
Total 100



SECTION I: Multiple Choice [20 Marks]

Notes: . For each multiple-choice question below, select only ONE answer. . Write your answer in your ANSWER BOOKLET (not this question sheet)
1.
[4] Which of the following statements is true? a) Probability mass function (pmf) can be used for both discrete and continuous random variables b) Cumulative distribution function (cdf) can be used for both discrete and continuous random

variables
c) Not all the moments of X can be calculated from the probability density function (pdf)
d) The value of the probability density function (pdf) cannot be greater than 1


2.
[4] Which of the following statements about independence is true? a) For two events A and B, if P[B]=0, then A and B cannot be independent b) If A and B are independent, then A and Bc are also independent c) If A and B are mutually exclusive with non-zero probability, then A and B are independent d) A1, A2, and A3 are independent if P[A1A2A3]=P[A1]P[A2]P[A3]

3.
[4] Let A and B be two sets. Which of the following is not true?


cc c

a) .A .B..A .B
cc c

b) A ..A .B...A .Bc .
c) P.A .B.. .. .PB

PA ..
d) P.A .B.. ...PB

PA ..

4. [4] Which of the following functions is a valid cdf?

(b)
(a)




(d)
(c)


5. [4] Which of the following is true? a) The expectation of a random variable cannot be negative b) Expectation is always one of the possible values a random variable can take c) The expectation of a function of a random variable equals the function of the expectation for that
random variable
d) For a discrete random variable X, E[g(X)] can be computed from the pmf of X


SECTION II: Problems [80 Marks]
Notes: . Write your solution in your ANSWER BOOKLET (not this question sheet)
1. [20 Marks] Suppose that a random variable X assumes integer values between 1 and 8 with the probability mass function (pmf) given in the table.
K 1 2 3 4 5 6 7 8
pX(k) 1/16 2/16 4/16 2/16 1/16 3/16 2/16 1/16

a) [4] Find P[3<X6] and P[1<X<6|X>2].
b) [4] Plot the cdf of X. Label important values on your plot.
c) [4] Find the expected value and variance of X.

d) [4] Find the conditional pmf of X, conditioning on the event A={3X7}.