STAT 100A MIDTERM EXAM Solution
Problem 1:Suppose we generate two independent random variables X and Y uniformly over [0, 1]. (1) (4 points) Calculate P (X 2 + Y 2 1). A: Let be the unit square [0, 1]2 , and let A be the event that X 2 + Y 2 1, th
Statistics 100A
Homework 3 -
Solutions
Exercise 1
Using the binomial theorem we have:
! = ! ! ! 1 ! = + 1
!
!
!
Exercise 2
This is a hypergeometric probability distribution problem.
a.
=
!
!
b.
=
!"
STAT 100A HWI Due next Wed in class
Problem 1: Suppose we ip a fair coin 4 times independently. (1) What is the sample space? (2) What is the set that corresponds to the event that the number of heads is 2? What is its probability? (3) Let Zi = 1 if
Fall2013 STATS 100A. INTRODUCTION TO PROBABILITY
4:00P-5:15P
WGYOUNG
CS24
Instructor: Li, Ker-Chau
Office: MS 8959 Office hours: Thursday 1:30pm to 2:30pm
e-mail : kcli@stat.ucla.edu
Final Examination Code: 09 - Monday, December 9, 2013, 8:00am-11:00am
Mi
Sample Exam, STAT100a
1. Tennis rackets from an oversea factory are packed into three boxes of 10, 20, 30
rackets respectively. An inspector found a broken racket. He decided to return the whole
box that contains the broken racket to the factory. Let X be
University of California, Los Angeles Department of Statistics Statistics 100A Exam 2 - Practice problems
Problem 1 Answer the following questions: a. The amount of snow during winter at a certain mountain in California follows the normal distribution wit
Stat 100 -Intro Probability
Homework 2
J. Sanchez
UCLA Department of Statistics
Instructions
(1) Homework must be stapled. Two columns not allowed.
(2) No late homework accepted under any circumstances. If R script le is requested, it must be uploaded bef
Bivariate and Multivariate Normal
1
Bivariate Normal
The bivariate normal pdf is given by
f (x, y ) =
1
2X Y
2
2
1
Joint density
2
2
xX
1
exp 2(12 )
+ yY Y
X
xX
X
y Y
Y
(1)
2
2
It has 5 parameters X , Y , X , Y , .
There is another nice way of expressing
More families of continuous random variables
Continuous Random Variables: The Gamma
Density,Uniform density, Density of functions of a
random variable
I. The Gamma
II. The Gamma random variable and its pdf.
III. The Uniform random variable.
Juana Sanchez
Homework 3.
Homework must be answered in the order shown here (else please make a note
telling the reader where it is).
Write your answers neatly
Work must be shown for full credit
No late homework accepted und
Statistics 100A
Homework 1
Exercise 1
Suppose that people are seated in a random manner in a row of
can two particular people and be seated next to each other?
Exercise 2
If people are seated in a random manner in a row containing
the people occupy adjace
University of California, Los Angeles Department of Statistics Statistics 100A Homework 2
EXERCISE 1 The Statistics Society at a large university would like to determine whether there is a relationship between a students interest in statistics and his or
STAT 100B Midterm Solution
Problem 1 Suppose X1 , X2 , ., Xn Exp(). The density function of Exp() is f (x) = ex for x 0, and f (x) = 0 for x < 0. (1) Suppose we want to estimate by solving the estimating equation Pr(X > 1) = m/n, where m is the n
Homework 1
Homework must be answered in the order shown here (else please make a note telling the
reader where it is).
Write your answers neatly
Work must be shown for full credit
No late homework accepted under any circumstances
1.- A die is rolled conti
Stat 100 -Intro Probability
Homework 7
J. Sanchez
UCLA Department of Statistics
Instructions
(1) Homework must be stapled. Two columns not allowed.
(2) No late homework accepted under any circumstances. (There is NO R script le requested for this homework
Stat 100 -Intro Probability
Homework 8
J. Sanchez
UCLA Department of Statistics
Instructions
(1) Homework must be stapled. Two columns not allowed.
(2) No late homework accepted under any circumstances. (There is NO R script le requested for this homework
Homework 1 key
1.- A die is rolled continually until a 6 appears, at which point the experiment stops. What is the sample
space of this experiment? Let En denote the event that n rolls are necessary to complete the experiment.
What points of the sample sp
Notes
Simulations in Probability
Juana Sanchez
jsanchez@stat.ucla.edu
UCLA Department of Statistics
J. Sanchez
Stat 100A. Simulations in Probability
Simulation with random numbers
Notes
I. Steps in a simulation and illustration with the lie detector examp
16.11.22
Variance of sum of two random variables,
Properties of covariances, The multinomial
distribution, The bivariate normal when
rho=0.
Juana Sanchez
UCLA Dept of Statistics
ccle.ucla.edu
Stat 100/Sanchez-Intro Probability
1
Definition of covariance,
Stat 100A -Intro Probability
Practice Final Exam
J. Sanchez
UCLA Department of Statistics
PLEASE DO THE FOLLOWING BEFORE YOU START
WRITE YOUR NAME and ID, AND BUBBLE THEM, ON THE SCANTRON. USE NO.2 PENCIL.
Write the COLOR of your exam in pencil on the t
Stat 100 -Intro Probability
Homework 5
J. Sanchez
UCLA Department of Statistics
PROVIDE THE INFORMATION REQUESTED IN THIS BOX:
LAST NAME: FIRST NAME: ID:
TODAYs DATE:
TAs NAME: , TIME OF YOUR TA SESSION:
Instructions
(1) YOU MUST WRITE YOUR ANSWERS IN
Notes
Random variables
Discrete Random Variables II
Juana Sanchez
jsanchez@stat.ucla.edu
UCLA Department of Statistics
J. Sanchez
Stat 100A Intro Probability
Outline
Notes
I. Some proofs of expectations and variance of linear functions of a
random variabl
Stat 100 -Intro Probability
Homework 2
J. Sanchez
UCLA Department of Statistics
PROVIDE THE INFORMATION REQUESTED IN THIS BOX (you lose 1 point for each item missing
or entered incorrectly:
LAST NAME: FIRST NAME: ID:
HWK DUE DATE:
TAs NAME: , TIME OF YO
Notes
Random variables
Discrete Random Variables III
Juana Sanchez
jsanchez@stat.ucla.edu
UCLA Department of Statistics
ccle.ucla.edu
J. Sanchez
Stat 100A Intro Probability
This lecture
Notes
The Poisson Random Variable
The Bernoulli r.v.
The Binomial r.v
Stat 100 -Intro Probability
Homework 2
J. Sanchez
UCLA Department of Statistics
PROVIDE THE INFORMATION REQUESTED IN THIS BOX (you lose 1 point for each item missing
or entered incorrectly:
LAST NAME: FIRST NAME: ID:
HWK DUE DATE:
TAs NAME: , TIME OF YO
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Stat 100 -Intro Probability
Homework 3
J. Sanchez
UCLA Department of Statistics
PROVIDE THE INFORMATION REQUESTED IN THIS BOX:
LAST NAME: FIRST NAME: ID:
TODAYs DATE:
TAs NAME: , TIME OF YOUR TA SESSION:
Instructions
(1) YOU MUST WRITE YOUR ANSWERS IN
Stat 100 -Intro Probability
Homework 5
J. Sanchez
UCLA Department of Statistics
PROVIDE THE INFORMATION REQUESTED IN THIS BOX:
LAST NAME: FIRST NAME: ID:
TODAYs DATE:
TAs NAME: , TIME OF YOUR TA SESSION:
Instructions
(1) YOU MUST WRITE YOUR ANSWERS IN
Stat 100 -Intro Probability
TA Session
J. Sanchez
UCLA Department of Statistics
Question 1. Someone computed the probability of the event (E B)(E F)c as being 0.6. Which of the following
events has the same probability? (Note: as we have said several time
Assessment of the Pedagogical
Utilization of the Statistics Online
Computational Resource in Introductory
Probability Courses: A quasi-experiment
Ivo Dinov(1,2)
Juana Sanchez(1)
UCLA Department of Statistics and
(2)
Center for Computational Biology
(1)
ht
Stat 100 -Intro Probability
Homework 9
J. Sanchez
UCLA Department of Statistics
PROVIDE THE INFORMATION REQUESTED IN THIS BOX:
LAST NAME:
FIRST NAME:
ID:
TODAYs DATE:
TAs NAME:
, TIME OF YOUR TA SESSION:
Instructions
(1) YOU MUST WRITE YOUR ANSWERS IN THE
Spring 2017- Reading homework 6- Due Friday, 4/28,before 11 PM. Must SUBMIT before 11 PM.
My sites / 17S-STATS100A-1 / HOMEWORK
/ Spring 2017- Reading homework 6- Due Friday, 4/28,before 11
PM. Must SUBMIT before 11 PM.
Started on
State
Completed on
Time
Stat 100 -Intro Probability
Homework 15
J. Sanchez
UCLA Department of Statistics
PROVIDE THE INFORMATION REQUESTED IN THIS BOX:
LAST NAME: FIRST NAME: ID:
TODAYs DATE:
TAs NAME: , TIME OF YOUR TA SESSION:
Instructions
(1) YOU MUST WRITE YOUR ANSWERS IN
HONR 399
October 25, 2010
Chapter 24 Answers
1. Consider the joint density of X and Y from Example 22.1 of Chapter 22, namely,
1
fX,Y (x, y) = (1 x2 )(3 y)
8
for 1 x 1 and 1 y 1,
and fX,Y (x, y) = 0 otherwise.
Find E[X].
The density of X is, for 1 x 1,
Z