ABCDEFGHIJKLMNOPQRSTUVWXYZAA
1
2
Links:Slides
https://robertmarks.org/Classes/EE5345-Slides/Slides.html
3
Sylabus
https://robertmarks.org/Classes/ENGR%205345/5345-Syllabus.pdf
4
Text
https://www.amazon.com/gp/product/B00ALTS9TY/
5
This Link
https://docs.google.com/spreadsheets/d/1Zueo5Zn2TJcLdTBLd9H1U8eWDX8wO-FT_OxTsejiRoY/edit?usp=sharing
6
7
ECS 5354
8
1January 19TuesHistory
Solve the unfinished game problem
https://youtu.be/FMmsinC9q6A
9
Due Jan 21
10
2January 21ThursReview
Solve the Deal or No Deal Problem
https://youtu.be/-OqhMVIrJOI
11
Solve the 5 presidents problem
12
Due Jan 28
14
3January 28ThursReview
Chapt 2- p89: 77,80 ;p92:104,105
https://youtu.be/m0q7QDDz5-0
15
Chapt 4 - p218: 26
16
Convert the MatLab erf to my erf. SOLUTION:
https://docs.google.com/document/d/1zPn3xWldlzPtqKMds98j02e01jvNvkDDp8vqK1OV0D4/edit?usp=sharing
17
Due Feb 4
18
4February 2TuesDistributions
https://youtu.be/9RezsChrzaU
19
Info Theory
20
5February 4ThursInfo Theory
Evaluate optimal "20 questions" queries for:
https://youtu.be/c7EmERRdq1I
21
p = 1/3, 1/3, 1/3 and p = 1/8, 3/8, 1/10, 2/10, 2/10 (hard)
22
Evaluate E(Questions) for each and 2^(-length_n) for each
23
Compare to the entropy in each case and comment.
24
Chapt 3 - p132: 13
25
Due Feb 11
26
6February 9Tues
RV Transformation
https://youtu.be/hPVmeQri_rc
27
7February 11Thurs
Functions of a RV
https://youtu.be/AAG-h8rh5BA
28
HOMEWORK:
Show g(x) = F_X transforms a continuous f_X RV to uniform RV
29
(a) What if X is a discrete RV? (b) a Posson RV?
30
Show inverse of F_X transforms a continuous uniform RV to an f_X RV
31
What if X is a discrete RV?
32
Find f_Y when X is uniform on (-pi/2,pi/2) and g(x)=tan(x)
33
Derive f_Y if X is zero mean Gaussian and (a) Y=|X|, (b) Y=X^2
34
Find g(x) to transform a centered Cauchy to a uniform RV
35
Due Feb 25
38
8February 23Tues
Characteristic Functions
https://youtu.be/skA9oyKv9fg
39
HOMEWORK:
40
Generate a bunch of Y from a uniform distribution X using a transformation Y=g(X)
41
Derive f_Y (y)
42
Generate a histogram of Y's, nomalize to unit area and compare to f_Y (y)
43
Due March 4
44
9February 25Thurs
Characteristic Functions
https://youtu.be/bC9Z9Ls5-bk
45
HOMEWORK:
46
What is the distribution when the RV's from the following RV's are added:
47
SIx geometric RV's all with given parameter p.
48
Six Bernoulli RV's all with paramenter p
49
Six Pascal Negative Binomial RV's all with parameter p but different r's
50
Three gaussians all with different means and variances
51
What is the mean and variance when the characteristic function is exp(- |omega| ^N) * exp(-j omega). N is an integer.
52
Due March 4
53
10March 2Tues2D RV's
https://youtu.be/hWINB89ezfQ
54
11March 4Thurs2D RV's
https://youtu.be/UZ68vjyesSc
55
HOMEWORK:
56
1. Chose a causal pdf (= 0 for negative x). Plot Pr[X>=a] versus E[X]/a as a function of a and verify Markov's inequality.
57
2. Chose a pdf. Plot Pr[ |X-E(X)|>a] versus var(X)/a^2 as a function of a and verify Chebyshev's inequality
58
3. Copy the 10x10 histogram on Sheet 2 of this spreadsheet.
59
(a) Calculate and generate a 2D plot of the corresponding empirical pdf. Make sure to have a number in each location of the 10x10 grid.
60
(b) Calculate and generate a 2D plot of the corresponding empirical cumulative distribution function
61
(c) Repeat (a) and (b) when we are given that
62
(i) 3<=X<=6 and 4<=Y<=6
63
(ii) X<Y
64
Due March 11
65
12March 9Tues2D RV's
https://youtu.be/V4PJUB5oKgc
66
13March 11ThursMD RV's
https://youtu.be/KvhONWbthtk
67
MIDTERM:
90
14March 16TuesMD RV's
https://youtu.be/XyDJnegwzR8
91
15March 18Thurs
Law of Large Numbers
https://youtu.be/pj8xdnSBcVw
92
Homework
93
1. Computer work: Randomly generate points in square. Inside the square is an inscribed circle.
94
(a) What is the probability a point will be in the circle?
95
(b) As each new point is added, keep track of and plot the percent of points in the circle divided by the thal number of points chosen.
96
(c) Does the limit of your plot approach your answer in (a)?
97
16March 23Tues
Central Limit Theorem
https://youtu.be/4AvCvR6SJyg
98
Homework
99
1. Computer work: Generate a bunch of empirical pdf's. For at least one, use a random number generator. Convolve these pdf's.
100
(a) Does the convolution have an area of one?
101
(b) Plot the convolution and the approximated gaussian in the same figure.
102
2. 1000 dollar amounts are rounded UP to the nearest dollar.
103
(a) Estimate the total probability the error is greater that $495. Give a number.
104
(b) Greater that $1000 dollars? Give a number.
105
17March 25Thurs
Confidence Intervals
https://youtu.be/oVTWKN5EVII
106
1. A roulette wheel has 37 slots. Two of them are green.
107
(a) Out of 10,000 tries, a ball rolls into a green slot 735 times. Generate a 95% percent confidence around the sample average 0.0735.
108
Assume we do not know the true value of p=2/37
109
(b) Does the true value of p =2/37 lie in this interval? Do you think the roulette wheel is fair?
110
18March 30Tues
Gaussian Processes
https://youtu.be/VAxUactaZeA
111
19April 1Thurs
Counting/Poisson Processes
https://youtu.be/_PtBsCW5srU
112
1. Cars go by at point on University Avernue at an average rate of 1 car every two seconds. What is the probability no cars go by in one second?
113
2. No cars go by for five seconds. What is the probability no cars go by after 6 seconds (i.e. one second more)?
114
20April 6TuesStationarity
https://youtu.be/0nYCwtVnOlw
115
Homework:
116
1. A sequence of iid uniform random numbers on (0,1) is convolved with a rectangular window of length 100. Call the resulting stochastic process X
117
(a) Calculate the mean, autocorrelation and autocovariance of X
SOLUTION:
https://docs.google.com/document/d/1zPn3xWldlzPtqKMds98j02e01jvNvkDDp8vqK1OV0D4/edit?usp=sharing
118
(b) Is X stationary in the wide sense?
119
(c) Is X Gaussian or close to Gaussian?
120
21April 8Thurs
Worked Homework
https://youtu.be/1QdpuESFdbg
121
22April 13Tues
Wide Sense Stationarity
https://youtu.be/azosXf_Pfpk
122
Homework:
123
1. Explain how you would estimate the autocorrelation of a stationary random process from an ensemble?
124
2. Computer work: Do this empicically for the stochastic process defined in Lecture 20
125
23April 15Thurs
Ergodicity / PSD
https://youtu.be/0xJkv86sewM