Online EE 131A
Homework #4 Solution
Fall 2010 K. Yao
1. X is a random variable with a binomial distribution with parameter n and p = 0.9 a. Prob. the system will declare an airplane = ( ) 2 P (1 X 2) = 1 - P (X = 0) = 1 - (0.9)0 (0.1)2 = 0.99 0 b. Prob. t
Online EE 131A 1. a. S = cfw_1, 2, 3, 4, 5, 6. b. A = cfw_2, 4, 6.
Homework #1 Solution
Fall 2010 K. Yao
c. Ac = cfw_1, 3, 5 "odd number of dots." 2. a. S = set of ordered pairs (x, y) where x, y cfw_1, 2, 3, 4, 5, 6. 1 2 3 4 5 6 1 (1,1) (2,1) (3,1) (4,1)
Online EE 131A
Homework #6 Due Nov. 10th
Fall 2010 K. Yao
Read Leon-Garcia (3rd edition), pp. 155-180; 255-278. 1. Problem 4.68, p. 222. 2. Problem 4.88, p. 223. 3. Let X be a Laplacian rv with a pdf given by fX (x) = (/2) exp(-|x|), 0 < , - < x < . Suppo
OLEE 131A
Homework #3 Due October 20th Read Leon-Garcia (3rd edition), pp. 96-104; 141-146,
Fall 2010 K. Yao
1. There are three power plants (denoted by i = 1, 2, 3) which can be either working or not working. If plant i is working, we denote it by ai = 1
EE 131A Probability
Professor Kung Yao Electrical Engineering Department University of California, Los Angeles M.S. On-Line Engineering Program Lecture 3 - 1
UCLA EE131A (KY)
1
Lecture 3 -1: More on counting (1) General Principle of Counting The most gene
EE 131A Probability
Professor Kung Yao Electrical Engineering Department University of California, Los Angeles M.S. On-Line Engineering Program Lecture 12-2
UCLA EE131A (KY) 1
Covariance (1)
The covariance of rv's X and Y provides a statistical average r
Online EE 131A
Homework #5 Due Nov. 3rd
Fall 2010 K. Yao
Read Leon-Garcia (3rd edition), pp. 148-188; 233-254. 1. Problem 4.63 (p. 221). 2. A limiter Y = g(X) is shown in Fig. P4.2 (p. 219). a. Find the cdf and pdf of Y in terms of the cdf FX (x) and pdf
EE 131A Probability
Professor Kung Yao Electrical Engineering Department University of California, Los Angeles M.S. On-Line Engineering Program Lecture 12-1
UCLA EE131A (KY) 1
Conditional expectation (1)
Review: For a rv X with a pdf fX(x), the expectati
EE 131A Probability
Professor Kung Yao Electrical Engineering Department University of California, Los Angeles M.S. On-Line Engineering Program Lecture 11-2
UCLA EE131A (KY) 1
Independence of two rv's (1)
Review: Two events A and B are independent if P(A
EE 131A Probability
Professor Kung Yao Electrical Engineering Department University of California, Los Angeles M.S. On-Line Engineering Program Lecture 11-1
UCLA EE131A (KY) 1
Jointly pdf and marginal pdf (1)
Let FXY(x,y) be the joint cdf of the joint rv
EE 131A Probability
Professor Kung Yao Electrical Engineering Department University of California, Los Angeles M.S. On-Line Engineering Program Lecture 10-2
UCLA EE131A (KY) 1
Jointly distribution of two rv's (1)
For a single rv X, it is fully characteri
EE 131A Probability
Professor Kung Yao Electrical Engineering Department University of California, Los Angeles M.S. On-Line Engineering Program Lecture 10-1
UCLA EE131A (KY) 1
Expectation of a function g(X) of X (1)
So far, we have considered the expecta
EE 131A Probability
Professor Kung Yao Electrical Engineering Department University of California, Los Angeles M.S. On-Line Engineering Program Lecture 3 - 2
UCLA EE131A (KY)
1
Lecture 3 -2: Axioms of probability (1) The theory of modern probability was d
EE 131A Probability
Professor Kung Yao Electrical Engineering Department University of California, Los Angeles M.S. On-Line Engineering Program Lecture 4-1
UCLA EE131A (KY) 1
Discrete sample space (1)
Suppose the sample space S = cfw_a1, ., an is finite.
EE 131A Probability
Professor Kung Yao Electrical Engineering Department University of California, Los Angeles M.S. On-Line Engineering Program Lecture 4-2
UCLA EE131A (KY) 1
Conditional Probability is a Probability
P(A|B) satisfies all the axioms of prob
EE 131A Probability
Professor Kung Yao Electrical Engineering Department University of California, Los Angeles M.S. On-Line Engineering Program Lecture 5-1
UCLA EE131A (KY) 1
Independence of Events (1)
Consider two events A and B. If the occurrence of eve
EE 131A Probability
Professor Kung Yao Electrical Engineering Department University of California, Los Angeles M.S. On-Line Engineering Program Lecture 5-2
UCLA EE131A (KY) 1
Binomial Probability Law (1)
Consider a binary-valued experiment with outcomes c
EE 131A Probability
Professor Kung Yao Electrical Engineering Department University of California, Los Angeles M.S. On-Line Engineering Program Lecture 6-1
UCLA EE131A (KY) 1
Random Variable (1)
So far, we have dealt with elementary outcomes and collecti
EE 131A
Probability
Instructor: Lara Dolecek
Discussion Set 3
Thursday January 21, 2016
and Friday January 22, 2016
Reading: Chapters 3 and 4 of Probability, Statistics, and Random Processes by A.
Leon-Garcia
1. Coin tossing example.
Problem 3.9, page 13
EE 131A
Probability
Instructor: Lara Dolecek
Discussion Set 2
Thursday January 14, 2016
and Friday January 15, 2016
Reading: Chapter 2 of Probability, Statistics, and Random Processes by A. Leon-Garcia
1. Conditional Probability. Problem 2.73, page 88 of
EE 131A
Probability and Statistics
Instructor: Lara Dolecek
TA: Ahmed Hareedy
Homework 2
Wednesday, January 13, 2016
Due: Monday, January 25, 2016
ahareedy@ucla.edu
Reading: Chapter 2
1. Consider a 26-key typewriter. Suppose that pushing a key results in
EE 131A Probability
Professor Kung Yao Electrical Engineering Department University of California, Los Angeles M.S. On-Line Engineering Program Lecture 9-2
UCLA EE131A (KY) 1
Second Moment (1)
The expectation of a rv X yields the mean . The second moment
EE 131A Probability
Professor Kung Yao Electrical Engineering Department University of California, Los Angeles M.S. On-Line Engineering Program Lecture 9-1
UCLA EE131A (KY) 1
Expectation (averaging) (1)
The cdf/pdf of a rv X completely characterizes the
OLEE 131A
Homework #3 Solution
Fall 2010 K. Yao
1. a.
b. P(X=0)=0.07; P(X=1)=.23; P(X=2)=0.57; P(X=3)=0.13. c.
d.
2. a. Ai = cfw_x : 0 x < 1. i=1
b. Since all the Ai 's are mutually exclusive, then Ai = . i=1 3. Solve for
n-2 2 n-2 C 2 C2 C0 C4 = 1 2C n n
Online EE 131A
Homework #1 Due Oct. 7th (Midnight PST)
Fall 2010 K. Yao
Read Leon-Garcia (3rd edition) Chap. 1 (pp. 1-17) and Chap. 2 (pp. 21-29; 41-47) 1. A die is tossed and the number of dots facing up is counted and noted. a. What is the sample space.
Online EE 131A
Homework #2 Due Oct 13th Read Leon-Garcia, 3rd ed. Chap. 2 (pp. 4766)
Fall 2010 K. Yao
1. From among ten employees, three are to be selected for travel to three out-of-town plants, A, B, and C, one to each plant. Since the plants are in dif
Online EE 131A
Homework #2 Solution
Fall 2010 K. Yao
1. There are 10 choices for plant A, but only 9 for plant B, and 8 for plant C. This give 10 a total of P3 = 10!/7! = 10 9 8 = 720 ways of assigning employees to the plants. 2. The number of ordering is
Online EE 131A
Homework #4 Due Oct. 27th Read Leon-Garcia (3rd edition), pp. 146-152; 163-180
Fall 2010 K. Yao
1. An air defense system consists of n independent radar sets over a given area. Assume each radar has a probability of 0.9 of detecting an airp
EE 131A Probability
Professor Kung Yao Electrical Engineering Department University of California, Los Angeles M.S. On-Line Engineering Program Lecture 6-2
UCLA EE131A (KY) 1
Cumulative Distribution Function (5)
Ex. 1. Toss a coin. Sample space S = cfw_H,
EE 131A Probability
Professor Kung Yao Electrical Engineering Department University of California, Los Angeles M.S. On-Line Engineering Program Lecture 6-3
UCLA EE131A (KY) 1
Continuous random variable (1)
A continuous random variable X is defined as a r