Homework 1 Due Monday, April 6th 2009
1. Read through the review material handouts found on my class website,
http:/www.uweb.ucsb.edu/~nbennett/PSTAT120B/120b.htm 2. Read Ch. 1, Sec 6.1-6.4 3. Hand
Homework 2 The updated version Due Monday, April 13th 2009 in class
1. Please ask questions if you do not understand something in lecture; I will do my best to answer your question. The goal of this
Homework 8 - Pstat 120B Winter 2017
Problem 1
An experimenter has prepared a drug dosage level that she claims will induce sleep for 80% of people
suffering from insomnia. After examining the dosage,
Confidence Intervals
Definition
A confidence interval for a confidence level is an interval inside which
the true but unknown parameter is with probability 1 . There are 3
types of confidence interval
Homework 9 Solution - Pstat 120B Winter 2017
Problem 1
Two sets of elementary school children were taught to read by using different methods, 50 by each method.
At the conclusion of the instructional
Homework 6 Solution - Pstat 120B Winter 2017
Problem 1
Let X1 ,X2 ,.,Xn denote a random sample of size n from a normal distribution with mean and variance
2 .
a) If is unknown and 2 is known, find the
Homework 7 - Pstat 120B Winter 2017
Problem 1
When it comes to advertising tweens are not ready for the hard-line messages that advertisers often use
to reach teenagers. The Geppeto Group study found
Hypothesis Testing
A hypothesis test is a tool to test the validity of a scientific/statistical
hypothesis.
As before, imagine that we are studying a random variable following a
distribution of known
Homework 3 Solution (120B F17)
7.11
P(| Y | 2) = P(1.5 Z 1.5) = 1 2P(Z > 1.5) = 1 2(.0668) = .8664.
7.12
We require P(| Y | 1) = P(.25 n Z .25 n ) = .90. This will be solved by
taking .25 n = 1.645, s
Homework 1 Solution (120B F17)
3.60
Let Y = # of fish that survive. Then, Y ~Bnomial(n = 20, p = .8).
a. P(Y = 14) = .109.
b. P(Y 10) = .999.
c. P(Y 16) = .589.
d. = 20(.8) = 16, 2 = 20(.8)(.2) = 3.2.
Homework 4 Solution (120B F17)
) aE( ) (1 a)E( ) a (1 a) .
8.6 a. E(
3
1
2
b. Var(3 ) a 2Var(1 ) (1 a) 2 Var(2 ) a 2 12 (1 a) 22 , since 1 and 2 are independent.
d
Var (3 ) 0 implies a 22 /( 12 22 )
Homework 2 Solution (120B F17)
6.20
a. The distribution of W is, FW (w) P(W w) P(Y 2 w) P(Y w ) FY ( w )
w 0 w 1.
b. The distribution of W is, FW (w) P(W w) P( Y w) P(Y w2 ) FY (w2 ) w 2 , 0 w 1.
6.3
Confidence Intervals
Definition
A confidence interval for a confidence level is an interval inside which
the true but unknown parameter is with probability 1 . There are 3
types of confidence interval
Introduction
Review of Pstat 120A
Pstat 120B - Fall 2016
Jacob Lundbeck Serup
Department of Statistics and Applied Probability, UCSB
September 26. 2016
Jacob Lundbeck Serup
Pstat 120B - Fall 2016
Intr
Transformations of Random Variables
Order Statistics
Sampling Distributions Related to the Normal Distribution
n m transformation
What do we mean by a transformation of a random variable?
Suppose:
I Y
Practice Jacobian and Order Statistics problems from the examples given in the book and related
homework problems.
Also for Chapter 7, it makes sense to go through the examples thoroughly. The midterm
PSTAT 120B - Probability & Statistics
Class # 05-1- Condence intervals
Jarad Niemi
University of California, Santa Barbara
26 April 2010
Jarad Niemi (UCSB)
Condence intervals
26 April 2010
1 / 18
Clas
Test topics
Distributions of functions of random variables
Method of distribution functions Alternative method of distribution functions Method of transformations Method of moment generating functions
PSTAT 120B - Probability & Statistics
Class # 04-1- Midterm Review I
Jarad Niemi
University of California, Santa Barbara
19 April 2010
Jarad Niemi (UCSB)
Midterm Review I
19 April 2010
1 / 26
Class ov
Homework 3 Due Friday, April 24th at 10am
1. Read the following sections 3.9, 4.9, 6.5, 6.7, 7.2, 7.3
2. Hand in the following problems: 4.136 page 206 4.140 page 206 6.37 page 322 6.40 page 323
Review of PSTAT 120A Spring 2009
Probability Measure (Probability Function) Given a sample space, S, a probability function, Pr[.], is a function satisfying the following three conditions: i) Non-neg
Useful Mathematical Tools Spring 2009
Summation Notation
Product Notation
Factorial Indicator Function Let be a space with elements . Let A be a subset of . Then the indicator function of A is giv
HW 1 Solutions
1.11 a. b. c.
c = c + c + + c = nc. cy ( x
i =1 i =1 n i i =1 n i
n
= c(y1 + + yn) = c yi
i =1
n
+ y i ) = x1 + y1 + x2 + y2 + + xn + yn = (x1 + x2 + + xn) + (y1 + y2 + + y
PSTAT 120B - Probability & Statistics
Class # 05-2- Small-sample condence intervals
Jarad Niemi
University of California, Santa Barbara
28 April 2010
Jarad Niemi (UCSB)
Small-sample condence intervals
PSTAT 120B - Probability & Statistics
Class # 08-1- Hypothesis testing
Jarad Niemi
University of California, Santa Barbara
17 May 2010
Jarad Niemi (UCSB)
Hypothesis testing
17 May 2010
1 / 19
Class ov
PSTAT 120B - Probability & Statistics
Class # 08-2- Sample size and CIs
Jarad Niemi
University of California, Santa Barbara
19 May 2010
Jarad Niemi (UCSB)
Sample size and CIs
19 May 2010
1 / 14
Class
PSTAT 120B - Probability & Statistics
Class # 08-3- P-values
Jarad Niemi
University of California, Santa Barbara
21 May 2010
Jarad Niemi (UCSB)
P-values
21 May 2010
1 / 15
Class overview
Announcements
PSTAT 120B - Probability & Statistics
Class # 09-1- Small sample tests
Jarad Niemi
University of California, Santa Barbara
24 May 2010
Jarad Niemi (UCSB)
Small sample tests
24 May 2010
1 / 16
Class ov
y
6.2 The distribution function of Yis FY(_v) : ICU 2)r2dr : (l x 2)(y3 1) , 1 3y 3 1.
1
a. FU1(u):P(U1Su)=P(3YSu):P(YSuf3):FY(uf3):%(u3HISl). Thus,
fU1(u):Fl(u):u2f18,3$u$3.
b. FU2(u):P(U2Su)=P(3YSu)