-
Notifications
You must be signed in to change notification settings - Fork 4
Expand file tree
/
Copy pathhomework.html
More file actions
322 lines (293 loc) · 20.3 KB
/
Copy pathhomework.html
File metadata and controls
322 lines (293 loc) · 20.3 KB
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8">
<meta http-equiv="X-UA-Compatible" content="IE=edge">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Stat 134, Spring '23 | Homework</title>
<!-- Bootstrap -->
<link href="https://fonts.googleapis.com/css?family=Raleway:400,700|PT+Serif|Lora" rel="stylesheet">
<link href="css/bootstrap.min.css" rel="stylesheet">
<link rel="stylesheet" type="text/css" href="css/main.css"/>
<!-- Swiper -->
<link rel="stylesheet" href="css/swiper.min.css">
<!-- jQuery -->
<script src="https://ajax.googleapis.com/ajax/libs/jquery/3.1.0/jquery.min.js"></script>
<!-- MathJax -->
<script type="text/x-mathjax-config">
MathJax.Hub.Config({tex2jax: {inlineMath: [['$','$'], ['\\(','\\)']]}});
</script>
<script type="text/javascript" async
src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS_CHTML">
</script>
<script src="https://use.fontawesome.com/63e7afe910.js"></script>
<!-- HTML5 shim and Respond.js for IE8 support of HTML5 elements and media queries -->
<!-- WARNING: Respond.js doesn't work if you view the page via file:// -->
<!--[if lt IE 9]>
<script src="https://oss.maxcdn.com/html5shiv/3.7.3/html5shiv.min.js"></script>
<script src="https://oss.maxcdn.com/respond/1.4.2/respond.min.js"></script>
<![endif]-->
</head>
<body>
<!-- Title -->
<div class="navbar navbar-custom">
<nav class="navbar">
<div class="container">
<div class="col-sm-3 col-xs-3" id=nav-text-left>
<div class=desktop>
<ul class="nav navbar-nav">
<li><h4><a href=index.html>Stat 134</a></h4></li>
</ul>
</div>
<div class=mobile>
<ul class="nav navbar-nav">
<li><h4><a href=index.html>134</a></h4></li>
</ul>
</div>
</div>
<div class="col-sm-9 col-xs-9" id=nav-text-right>
<ul class="nav navbar-nav navbar-right">
<li><p><a href=index.html>Index/Calendar</a></p></li>
<li><p><a href=homework.html>Homework</a></p></li>
<li><p><a href=readings.html>Readings</a></p></li>
<li><p><a href=syllabus.html>Syllabus</a></p></li>
<li><p><a href=staff.html>Staff/Section/OH</a></p></li>
</ul>
</div>
</div>
</nav>
</div>
<header class="container">
<h1 class = "header-xs">Concepts of Probability</h1>
<h5 class = "header-xs" id=subheading>Stat 134 with Adam Lucas, Spring '23.</h5>
</header>
<br>
<br>
<hr>
<br>
<header class="container">
<h3 class = "header-xs">Homework Logistics</h3>
</header>
<section class="container">
<ul class=logistics>
<li><p><b>Submission:</b> Homework is due by 11:59 pm on Gradescope. Late submissions will not be accepted. </p></li>
<li><p><b>Grading:</b> Submissions will be graded on a 0/1 scale. Each assignment will consist of 8 problems. A good attempt at 6 or more problems will receive the score of 1; anything else will get 0. Course staff will define what constitutes a "good attempt." We will be looking for reasoning and detailed work shown – it is assumed that you will show work or provide reasoning whether or not the question asks for it.</p> <p>Your lowest two homework scores will be dropped.</p></li>
<li><p><b>Academic Honesty:</b> Cheating will not be tolerated. While you are encouraged to work with other people, you must write up your own solutions.</p></li>
</ul>
</section>
<header class="container">
<h3 class = "header-xs">Recommended Strategy</h3>
</header>
<section class="container">
<ul class=logistics>
<li><p><b>Step 1</b>: Go through lecture notes and/or skim the text (see the <a href=readings.html>Reading</a> page). This is important. Note what the main ideas are and what techniques are being used in the examples. Read the text more carefully if you don't follow the examples.
</p></li>
<li><p><b>Step 2</b>: Try a problem.</p></li>
<li><p><b>Step 3</b>: If you get stuck, return to Step 1.</p></li>
<li><p>Iterate a couple of times, reading more carefully each time and trying the same problem. Most likely you'll be able to solve it. If you still can't, only then proceed to Step 4.</p></li>
<li><p><b>Step 4</b>: Move to another problem and seek help with the one that is giving trouble.</p></li>
<li><p>In our experience many students start with Step 2 and, if they get stuck, proceed immediately to Step 4. <b>This method is inefficient and doesn't result in much learning</b>. Before you come to the instructors or to the Student Learning Center, do the reading first! You may not need to make the trip at all.</p></li>
</ul>
</section>
<header class="container">
<h3 class = "header-xs">Assignments/ Practice Problems</h3>
</header>
<section class="container">
<p id=notation>In what follows, Exercise x.y.n is Problem n in the Exercises at the end of Section x.y. Exercise x.rev.n is Problem n in the Review Exercises at the end of Chapter x.</p>
<div class="homework">
<ul><h4>Homework 1</h4>
<li><b>Homework</b> (due <b>Friday, 1/27</b>)</li>
<li id="problems">1.1.8, 1.3.12, 1.4.6, 1.4.10, 1.5.2, 1.5.4, 1.6.6, 1.rev.16</li>
<li><b>Minimal Practice</b></li>
<li id="problems">1.1.7 (Example 2 will help), 1.3.3, 1.3.5, 1.3.7, 1.4.3, 1.4.5, 1.5.1, 1.5.5, 1.6.1, 1.6.5, 1.6.7a, 1. rev.7 (part d is on the next page)</li>
<li><b>Highly Recommended</b></li>
<li id="problems">1.3.6, 1.3.10, 1.3.11, 1.3.13, 1.5.6, 1.6.8, 1.rev.8, 1.rev.11, 1.rev.12, 1.rev.14, 1.rev.15, 1.rev.19</li>
</ul>
<br>
<ul><h4>Homework 2</h4>
<li><b>Homework</b> (due <b>Wednesday, 2/01</b>)</li>
<li id="problems">2.1.4, 2.1.6, 2.1.8, 2.1.12, 2.2.6, 2.2.10, 2.2.14, 2.rev.24 (be careful in part b!)</li>
<li><b>Minimal Practice</b></li>
<li id="problems">2.1.1, 2.1.3, 2.1.5, 2.2.1, 2.2.5, 2.2.9</li>
<li><b>Highly Recommended</b></li>
<li id="problems">2.1.2, 2.1.7, 2.1.9, 2.1.10, 2.1.11, 2.2.2, 2.2.3, 2.2.4, 2.2.8, 2.2.12, 2.rev.8</li>
</ul>
<br>
<ul><h4>Homework 3</h4>
<li><b>Homework</b> (due <b>Wednesday, 2/08</b>)</b></li>
<li id="problems">2.4.1a,d (just those two parts; show some of your calculations), 2.4.6, 2.4.8, 2.5.6, 2.5.8, 2.5.12a-e (just those five parts), 2.rev.10, 2.rev.18</li>
<li><b>Minimal Practice</b></li>
<li id="problems">2.4.3, 2.4.5, 2.4.7, 2.5.1, 2.5.7, 2.rev.15</li>
<li><b>Highly Recommended</b></li>
<li id="problems">2.4.2, 2.4.9, 2.5.2, 2.5.3, 2.5.4, 2.5.5, 2.5.9, 2.5.12 (the parts that aren't assigned for homework), 2.5.13, 2.rev.12, 2.rev.14, 2.rev.16, 2.rev.22, 2.rev.28</li>
</ul>
<br>
<ul><h4>Homework 4</h4>
<li><b>Homework</b> (due <b>Wednesday 2/15</b>)</li>
<li id="problems">3.1.8, 3.1.12, 3.1.14, 3.2.4, 3.2.14, 3.2.20, 3.rev.8, 3.rev.10</li>
<li><b>Minimal Practice</b></li>
<li id="problems">3.1.3, 3.1.9, 3.1.15 (connect this with Example 3 of Section 1.1 and Exercise 1.1.8), 3.2.1, 3.2.3, 3.2.5, 3.2.7, 3.2.11</li>
<li><b>Highly Recommended</b></li>
<li id="problems">3.1.2, 3.1.6, 3.1.7, 3.1.10, 3.1.13, 3.2.6, 3.2.9, 3.2.13, 3.2.17, 3.2.16, 3.2.19</li>
</ul>
<br>
<ul><h4>Homework 5</h4>
<li><b>Homework</b> (due <b>Wednesday, 2/22</b>)</li>
<li id="problems">3.3.6, 3.3.8, 3.3.12, 3.3.16, 3.3.20, 3.6.2 (turn the page for part d), 3.6.5, 3.6.6</li>
<li><b>Minimal Practice</b></li>
<li id="problems">3.3.1, 3.3.3, 3.3.13, 3.3.19, 3.6.1, 3.6.7, 3.6.8</li>
<li><b>Highly Recommended</b></li>
<li id="problems">3.3.5, 3.3.7, 3.3.9, 3.3.15, 3.3.23, 3.6.9</li>
</ul>
<br>
<ul><h4>Homework 6</h4>
<li><b>Homework</b> (due <b>Monday, 2/27</b>)</li>
<li id="problems">3.4.10, 3.4.12, 3.4.14, 3.5.4, 3.5.10, 3.5.12, 3.5.17, 3.rev.2<br></li>
<li><b>Minimal Practice</b></li>
<li id="problems">3.4.1, 3.4.3, 3.4.5, 3.5.1, 3.5.5, 3.5.11, 3.rev.15</li>
<li><b>Highly Recommended</b></li>
<li id="problems">3.4.2, 3.4.11, 3.5.2, 3.5.7, 3.5.9, 3.5.16, 3.rev.26</li>
</ul>
<ul><h4>Homework 7</h4>
<li>Due to the midterm, there will be no homework assigned this week. Enjoy the short break!</li>
</ul>
<br>
<ul><h4>Homework 8</h4>
<li><b>Homework</b> (due <b>Wednesday, 3/15</b>)</li>
<li id="problems">4.1.4, 4.1.7 (yes, it's an odd-numbered problem), 4.1.8, 4.1.12, 4.2.4, 4.2.8, 4.rev.2, 4.rev.14 (part c is on the next page)<br>
Note: Careful about the variance calculation in 4.2.8. Many students calculate the expectation by weighted averaging, but that doesn't work for variances. If you can do part (a), then you should be able to find the density via the c.d.f. Use that to justify your expectation calculation, and then use the same method to find the expectation of the square of X. After that the variance is easy.</li>
<li><b>Minimal Practice</b></li>
<li id="problems">4.1.1, 4.1.3, 4.1.9, 4.2.1, 4.2.5, 4.rev.3, 4.rev.13</li>
<li><b>Highly Recommended</b></li>
<li id="problems">4.1.2, 4.1.5, 4.1.10, 4.1.11, 4.2.6, 4.rev.4, 4.rev.12</li>
</ul>
<ul><h4>Homework 9</h4>
<li><i>Note:</i> MGF.x refers to problem x on the following worksheet: <a href="assets/extra_resources/mgf_problems.pdf" target="_blank">MGF Problems</a></li>
<li><b>Homework</b> (due <b>Wednesday, 3/22</b>)</li>
<li id="problems">4.4.2, 4.4.4, 4.4.6, 4.5.2, 4.5.6, 4.rev.4 (please provide a sketch of the density), MGF.1, MGF.4</li>
<li><b>Minimal Practice</b></li>
<li id="problems">4.4.1, 4.4.3, 4.4.7, 4.5.3, 4.5.5, 4.5.8, 4.6.1, 4.rev.5, 4.rev.18, 4.rev.21, 4.rev.22, MGF.2, MGF.5</li>
<li><b>Highly Recommended</b></li>
<li id="problems">4.4.5, 4.4.10, 4.5.4, 4.5.7, 4.rev.6, 4.rev.22, 4.rev.23, MGF.3</li>
</ul>
<ul><h4>Homework 10</h4>
<li><b>Homework</b> (due <b>Wednesday, 4/05</b>)</li>
<li id="problems">4.6.2, 4.rev.16, 5.1.4, 5.1.6, 5.1.9 (let the stick have length 1; try drawing the right region), 5.2.6, 5.2.8, 5.2.12, 5.2.14, 5.2.16</li>
<li><b>Minimal Practice</b></li>
<li id="problems">4.6.1, 4.6.5a, 4.rev.5, 4.rev.11 (do <b>not</b> crank them out by calculus; use what you know gamma and beta densities), 5.1.1, 5.1.7, 5.2.1, 5.2.3, 5.2.5, 5.2.11</li>
<li><b>Highly Recommended</b></li>
<li id="problems">4.6.3abcd, 4.6.5a-b, 5.1.2, 5.1.3, 5.2.4, 5.2.9, 5.2.10, 5.2.13, 5.rev.2</li>
</ul>
<ul><h4>Homework 11</h4>
<li><b>Homework</b> (due <b>Wednesday, 4/12</b>)</li>
<li id="problems">5.3.4, 5.3.8, 5.3.12, 5.4.10 (the easiest way is to use the c.d.f.), 5.4.13. 5.rev.12, 5.rev.22, 5.rev.24 (assume d < s; note that parts b and c are on the next page)</li>
<li><b>Minimal Practice</b></li>
<li id="problems">5.3.1, 5.3.3, 5.3.7 (turn page for more parts), 5.3.9, 5.3.11, 5.4.1, 5.4.3, 5.4.5, 5.rev.5</li>
<li><b>Highly Recommended</b></li>
<li id="problems">5.3.6 (it is helpful to draw figures as in 5.3.1), 5.4.4, 5.rev.2, 5.rev.16</li>
</ul>
<ul><h4>Homework 12</h4>
<li><b>Homework</b> (due <b>Wednesday, 4/19</b>)</li>
<li id="problems">6.1.2, 6.1.8, 6.2.4 (for part (b), I recommend looking at page 487 where you will find the variance of a useful uniform variable), 6.2.10, 6.2.12, 6.2.16, 6.3.2, 6.3.4</li>
<li><b>Minimal Practice</b></li>
<li id="problems">6.1.1, 6.1.3, 6.2.1, 6.2.3, 6.2.11, 6.3.1, 6.3.5</li>
<li><b>Highly Recommended</b></li>
<li id="problems">6.1.5, 6.1.7, 6.1.8, 6.2.7, 6.2.18, 6.3.3, 6.3.7</li>
</ul>
<ul><h4>Homework 13</h4>
<li><b>Homework</b> (due <b>Friday, 4/28</b>)</li>
<li id="problems">6.3.8, 6.3.10, 6.3.12, 6.4.8, 6.4.10, 6.4.12, 6.4.22, 6.rev.21</li>
<li><b>Minimal Practice</b></li>
<li id="problems">6.4.3, 6.4.5, 6.4.9, 6.4.11, 6.4.19, 6.4.21</li>
<li><b>Highly Recommended</b></li>
<li id="problems">6.4.7, 6.4.11, 6.4.13, 6.4.15a-c (don't redo (a) to prove (b) - <b>use</b> (a) to prove (b)!)</li>
</ul>
<ul><h4>Homework 14</h4>
<li>There will be no homework due this week, as this would be due during final week.</li>
<li><b>Highly Recommended</b></li>
<li id="problems">6.5.1, 6.5.2, 6.5.3, 6.5.4, 6.5.5, 6.5.6, 6.5.8, 6.5.12</li>
</ul>
<!-- <ul><h4>Homework 8</h4>
<li><b>Homework</b></li>
<li id="problems">4.1.4, 4.1.6, 4.1.12, 4.2.4, 4.2.6, 4.2.8, 4.rev.12, 4.rev.14 (part c. is on the next page)<br></li>
<li id="problems"><b>Note:</b> Careful about the variance calculation in 4.2.8. Many students
calculate the expectation by weighted averaging, but that doesn't work for
variances. If you can do part (a), then you should be able to find the density
via the c.d.f. Use that to justify your expectation calculation, and then
use the same method to find the expectation of the square of <i>X</i>. After
that the variance is easy</li>
<li><b>Minimal Practice</b></li>
<li id="problems">4.1.1, 4.1.2, 4.1.8, 4.1.9, 4.2.1,
4.2.5, 4.rev.3, 4.rev.13</li>
<li><b>Highly Recommended</b></li>
<li id="problems">4.1.5, 4.1.7, 4.1.11, 4.1.13, 4.1.14, 4.2.10, 4.2.14, 4.rev.4,
4.rev.12</li>
</ul>
<br>
<ul><h4>Homework 9</h4>
<li><b>Homework</b></li>
<li id="problems"> 4.4.2, 4.4.4, 4.4.6, 4.5.2, 4.5.6, 4.5.8, 4.rev.22, 4.rev.24<br></li>
<li><b>Minimal Practice</b></li>
<li id="problems">4.4.1, 4.4.3, 4.4.7, 4.5.3, 4.5.5, 4.6.1, 4.rev.2, 4.rev.5, 4.rev.18, 4.rev.21</li>
<li><b>Highly Recommended</b></li>
<li id="problems">4.4.5, 4.4.10, 4.5.4, 4.5.7, 4.5.9, 4.rev.6, 4.rev.7, 4.rev.23</li>
</ul>
<br>
<ul><h4>Homework 10</h4>
<li><b>Homework</b> (due <b>Wednesday, 11/1</b>)</li>
<li id="problems">4.6.2, 5.1.4, 5.1.6, 5.2.4, 5.2.8, 5.2.12,
5.2.14, 5.2.16<br></li>
<li><b>Minimal Practice</b></li>
<li id="problems">4.6.1, 4.6.5 a, 4.rev.5, 4.rev.11 (do <b><i>not</i></b> crank them out by calculus; use what you know gamma and beta densities), 5.1.1, 5.1.7, 5.2.1, 5.2.3, 5.2.5, 5.2.11</li>
<li><b>Highly Recommended</b></li>
<li id="problems">4.6.3 abcd, 4.6.5 ab, 5.1.2, 5.1.3, 5.1.8, 5.1.9 (let the stick have length 1; try drawing the right region), 5.2.6, 5.2.9, 5.2.10, 5.2.13, 5.rev.2</li>
</ul>
<br>
<ul><h4>Homework 11</h4>
<li><b>Homework</b> (due <b>Wednesday, 11/8</b>)</li>
<li id="problems">5.3.4, 5.3.8, 5.3.12, 5.rev.10, 5.rev.12, 5.rev.24 (assume <i>d < s</i>; note that parts b
and c are on the next page), 6.1.2, 6.1.8</li>
<li><b>Minimal Practice</b></li>
<li id="problems">5.3.1, 5.3.3, 5.3.7 (turn page for more parts), 5.3.9, 5.3.11, 5.rev.5, 6.1.1, 6.1.3</li>
<li><b>Highly Recommended</b></li>
<li id="problems">5.3.6 (it is helpful to draw figures as in 5.3.1), 5.rev.2, 5.rev.3, 5.rev.19, 6.1.5, 6.1.7</li>
</ul>
<br>
<ul><h4>Homework 12</h4>
<li>Because of Veteran's Day, I'm making this a short assignment. The next (and last) HW will be long, due the Wednesday after Thanksgiving. They will each count as a regular assignment. I'm putting 6.3 problems in the recommended but I'm not making you hand any in because I'm not sure how far I'll get in 6.3 in Monday's lecture. The last assignment will include 6.3, 6.4, and 6.5.</li>
<li><b>Homework</b> (due <b>Wednesday, 11/15</b>)</li>
<li id="problems">6.2.4 (for part (b), see page 487 for the variance of a discrete uniform), 6.2.10, 6.2.12, 6.2.16</li>
<li><b>Minimal Practice</b></li>
<li id="problems"> 6.2.1, 6.2.3, 6.2.11, 6.3.1, 6.3.5</li>
<li><b>Highly Recommended</b></li>
<li id="problems"> 6.2.7, 6.2.18 (done in class), 6.3.3, 6.3.7</li>
</ul>
<br>
<ul><h4>Homework 13/14</h4>
<li><b>Homework</b> (due <b>Wednesday, 11/29</b>)</li>
<li id="problems"> 6.3.2, 6.3.4, 6.3.8, 6.3.10, 6.3.12, 6.4.8, 6.4.10, 6.4.12, 6.4.22, 6.5.4, 6.5.6, 6.5.8</li>
<li><b>Minimal Practice</b></li>
<li id="problems">6.4.3, 6.4.5, 6.4.9, 6.4.11, 6.4.19, 6.4.21, 6.5.1, 6.5.3, 6.5.5</li>
<li><b>Highly Recommended</b></li>
<li id="problems"> 6.4.7, 6.4.11, 6.4.13, 6.4.15a-c (don't redo (a) to prove (b) - <i>use</i> (a) to prove (b)!), 6.5.2</li>
</ul>
<ul><h4>Homework 15</h4>
<li><p>There is no homework this week since next week is RRR week but it is important for you to get some practice on solving problems from Ch 5.4. We highly recommend you work on all the following problems.</p></li>
<li><b>Minimal Practice</b></li>
<li id="problems">5.4.1, 5.4.3, 5.4.5</li>
<li><b>Highly Recommended</b></li>
<li id="problems">5.4.4, 5.4.10 (the easiest way is to use the c.d.f.), 5.4.13</li>
<li>Anything we ask on the final will be highly similar to one of these problems. Maybe a different context, but very close to these problems.</li>
</ul> -->
</div></section>
<hr>
<footer section="container">
<row class="col-sm-12">
<ul class="col-sm-12">
<li>Site originally designed and developed by <a href="https://www.stat.berkeley.edu/~ani/.com" target="_blank">Ani Adhikari</a> and <a href="http://andypalan.com" target="_blank">Andy Palan</a>. </li>
<br>
</ul>
</row>
</footer>
</body>
</html>