Stat20:LecSec2.Spring2014.HowardDAbreraMIDTERMScore:[/60]
NAME:_(AsonBearfacts)SID:_
Signature: _ GSI:_ Section time: _
Instructions: Fill in all applicable answers and give reasons/show work where required.
_
1. A continuous random variable X has a cumul
Introduction
A histogram is a graph that summarizes data.
How to read histograms
A histogram does not need a vertical
scale.
But there is a horizontal scale.
Example: The incomes from 50,000 American families in 1973.
Basic properties
The histogram: a
Prepared by Anshuman Tiwari
Statistics 20
Midterm Review Exercises part 2 Solutions
For questions 1 through 3, show your work. I roll three six-sided, fair dice. What is the
probability that:
1. All three dice show the same number (such as 4, 4, 4 or 2, 2
Summation and Correlation
The correlation coecient r can be written either
1 n (xi x) (yi y )
n i=1
SDx
SDy
n
i=1
1
n
or
xi y i xy
SDx SDy
The proof is as follows:
1 n (xi x) (yi y )
n i=1
SDx
SDy
=
=
=
=
n
1
n SDx SDy
1
SDx SDy
1
n
n
i=1
n
1
=
n SDx SDy
Solutions to Review Problems
Chapter 3:
Review Exercises 6, 7, 8, 9.
6. Lists (i) and (ii) have this histogram but list (iii) does not this is because
lists (i) and (ii) both have 25% of the people between 66.5 and 67.5 inches,
50% of the people between 6
Sec time: I
l-
STAT 20: Spring 2015: QUIZ 1: My GSI is:
Name: 90] " Gimp/V]
Score: I30
SID:
The table below shows the distribution of ages in a population of people less than 74 years.
The intervals include the right endpoint. When a histogram is drawn as
Stats 20 Introduction to Probability and Statistics Lecture 3 Notes
Example: High School Hobbies
(Hypothetical:) Imagine we are interested in exploring what kindsof hobbies high school students
have below. We construct a survey:
(1) Circle your gender: Fe
Stats 20 Introduction to Probability and Statistics Lecture 1 Notes
Example 1: New Antiperspirant
(Hypothetical) A new women's antiperspirant has been developed. We are interested in
determining if it actually impedes perspiration. How do we do this?
Use
Exam 1
Instructor: Tessa Childers-Day
Stat 20
Please write your name and student ID below, and circle your section. With your
signature, you certify that you have not observed poor or dishonest conduct on the part of
your classmates. You also certify that
Stats 20 Introduction to Probability and Statistics Lecture 2 Notes
Studies and Surveys
Differences
o
Observational Study: attempts to isolate the effect of a change/manipulationcfw_but
investigator does not control the manipulation, only observes it
o
Sa
Final Exam
Instructor: Tessa Childers-Day
Stat 20
9 August 2012
Please write your name and student ID below, and circle your section. With your
signature, you certify that you have not observed poor or dishonest conduct on the part of
your classmates. You
Final Exam
Instructor: Tessa Childers-Day
Stat 20
15 August 2013
Please write your name and student ID below, and circle your section. With your
signature, you certify that you have not observed poor or dishonest conduct on the part of
your classmates. Yo
Midterm Exam
Instructor: Tessa Childers-Day
Stat 20
1 May 2014
Please write your name and student ID below, and circle your section. With your
signature, you certify that you have not observed poor or dishonest conduct on the part of
your classmates. You
Midterm Exam
Instructor: Tessa Childers-Day
Stat 20
11 March 2014
Please write your name and student ID below, and circle your section. With your
signature, you certify that you have not observed poor or dishonest conduct on the part of
your classmates. Y
Midterm Exam
Instructor: Tessa Childers-Day
Stat 20
18 July 2013
Please write your name and student ID below, and circle your section. With your
signature, you certify that you have not observed poor or dishonest conduct on the part of
your classmates. Yo
Midterm Exam
Instructor: Tessa Childers-Day
Stat 20
12 July 2012
Please write your name and student ID below, and circle your section. With your
signature, you certify that you have not observed poor or dishonest conduct on the part of
your classmates. Yo
Stat 20: Intro to Probability and Statistics
Lecture 7: Measurement Error
Tessa L. Childers-Day
UC Berkeley
2 July 2014
Todays Goals
Repeated Measurements
Outliers
Errors
By the end of this lecture.
You will be able to:
Explain why we measure repeatedly
C
Stat 20: Intro to Probability and Statistics
Lecture 8: Bivariate Data and Correlation
Tessa L. Childers-Day
UC Berkeley
3 July 2014
Todays Goals
Summary Statistics
Association
Correlation
Properties
By the end of this lecture.
You will be able to:
Constr
T9¢( ® 9:61:er THE LAST Resume LEcTu as
(b) In a television documentary "Wings of the Storm" (about Australian
Air Crew who participated in the bomber operations against German!
6%; in World War II, screened on the ABC during April 1983) the
following sta
0.25
P(X=x)
0.2
0.15
0.1
0.05
0
0
x
1
P(X=x)
2
3
4
Value (x)
5
6
7
8
9
x.P(X=x)
0
1
2
3
4
5
6
7
8
9
Totals
This is the distribution of the
number of heads when a fair
coin is tossed n=9 times.
(1) The sum of the probabilities should equal 1 (check this)
(
Stat 20 PDF and CDF
Probability Density Function (PDF)
Definition:
In pdfs, the area under the graph represents probabilities. For a pdf, the total area under the graph is 1. Why?
Continuous random variable X has PDF f(x) if
b
P(a x b) =
f ( x ) dx
a
a
f
7 FALL 1006:
STAT 2 : Sec 2
Course mark
before Final
(60)
Highest Mark
90th Percentile
80th Percentile
70th Percentile
60th Percentile
Median
40th Percentile
30th Percentile
20th Percentile
10th Percentile
Lowest Mark
PNE = 43'5 2
Prepared by Anshuman Tiwari
Statistics 20
Midterm Review Questions 2
For questions 1 through 3, show your work. I roll three six-sided, fair dice. What is the
probability that:
1. All three dice show the same number (such as 4, 4, 4 or 2, 2, 2)?
2. All th
HW07 - More Probability
Stat 20 & 131A, Spring 2017, Prof. Sanchez
Due Mar-9
1) True or false, and explain:
0.4pts
Give 0.2 pts for each part. Total 0.4 pts.
a. If a die is rolled three times, the chance of getting at least one ace is 1/6 + 1/6 + 1/6 = 1/
HW09 - Probability Histograms and Sampling
Stat 20 & 131A, Spring 2017, Prof. Sanchez
Due Mar-23
1) A coin is tossed 100 times. Use normal approximation (with continuity correction) to estimate
the chance of getting 60 heads. Please show your work (no wor
Practice Problems (for midterm 2)
Spring 2017
1) In Lotto 6-53, there is a box with 53 balls, numbered from 1 to 53. Six balls are drawn at random
without replacement from the box. You win the grand prize if the numbers on your lottery ticket
are the same
HW08 - Chance Variability
Stat 20 & 131A, Spring 2017, Prof. Sanchez
Due Mar-16
1) One hundred draws are made at random with replacement from the box [1, 2].
0.5pts
Give 0.1 pt for each part. Total 0.5 pts.
a. How small can the sum be?
The smallest sum is
Practice Problems (for midterm 2)
Spring 2017
1) In Lotto 6-53, there is a box with 53 balls, numbered from 1 to 53. Six balls are drawn at random
without replacement from the box. You win the grand prize if the numbers on your lottery ticket
are the same