Statistics 134, Fall 2002 FINAL EXAM
Name: SID number:
Prof. Pitman
SHOW CALCULATIONS, OR GIVE REASONS, ON ALL PARTS OF ALL QUESTIONS. DO NOT LEAVE NUMERICAL ANSWERS UNSIMPLIFIED. You may refer to your text and class materials.
1 2 3 4 5 6 7 8 9 10
Total
SECTION 8/9: Exercises
8.3
Nigel Corporation operates two childcare centers in two different areas of Miami. The
company wants to estimate the percentages of parents who think that childcare delivered
at each of these facilities is excellent. A sample of
Solution for HW5
Q.54
(a) Noting that
n
i=1 Xi
P oisson(n)
n
f (X1 , X2 , , Xn |
n
i=1
Xi ) =
Xi n
e
n
i=1 xi !
i=1
n
Xi n
e
n
i=1 Xi )!
n
=(
Xi )!
xi !
i=1
(1)
i=1
n
i=1 Xi
(1) doesnt depend on the parameter . Thus,
factorization lemma.
(b)
n
i=1
(
is
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t f ts p tl j
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k
k
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Theory of Statistics.
Homework V February 25, 2002. MT
8.17.c
When is known, = X is an unbiased estimator for . If you can show that its ^
variance attains the Cramer-Rao lower bound, then no other unbiased estimator can have lower variance. Calculations
e
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X wnX X ' X g
The Solution of Homework #5
Chapter 8
Exercise 11
a. The probability that the newborn's birth weight is less than 2500 grams is
X 3500 2500 3500 P ( X 2500) P P( Z 2.34) 0.01 430 430 b. The value Z 1.645 cuts off the lower 5% of the standard normal curve
9. Let X1 , .Xn be iid from Poisson distribution with parameter . We will use bootstrap ^ to find standard error of MLE of , that is = X. ^ 1. Generate M samples of sample size n from Poisson distribution with parameter . 2. For each sample calculate aver
% q v% s P q %Bt s 8% m r8 ~ d t ~ 8 3 y ~ e n g g rg e f t BFqkRfve ' F y t j d8F qniq n i r8 ~ w v i R i jvmghj f y h j 5 j t cv i g v g8mBjvdkv8%r8 ~ t ~ gqdhqlhc r m g i gmgh gfYqn B8 i h8g f d P t F r e g 5 vdkvB t g g n l qcB 8 u ~ $w i ~ % qh iqg
Descriptive statistics
Stat 135
UC Berkeley
Summer 2012
Stat 135
Descriptive statistics
The CDF
The cumulative distribution function (CDF ) of a random variable
X is
F (x ) P (X x ).
(1)
If the random variable is continuous, then f (x ), the derivative of
Hypothesis testing
Stat 135
UC Berkeley
Summer 2012
Stat 135
Hypothesis testing
Example: Two coins
I have two coins:
Coin 0 has probability of heads 0.5
Coin 1 has probability of heads 0.7
I choose a coin, toss it ten times, and tell you the number of
hea
Survey sampling
Stat 135
UC Berkeley
Summer 2012
Stat 135
Survey sampling
Bias and chance error
Estimate from sample = Population value + bias + chance error.
Bias means the expected value for the sample is dierent from the
population value, due to some s
SECTION 5: Exercises
5.1*
Find the area under the standard normal curve.
a. between z = 0 and z = 1.90
c. between z = 1.25 and z = 2.37
e. from z = -1.67 to z = 2.34
b.
d.
between z = 0 and z = -1.75
between z = -1.53 and z = -2.78
5.2
Obtain the followin
Supercrunchers Chapter 6
Questions
1. Be prepared to discuss the process that Acxiom and ChoicePoint use to build their databases.
The author provides a good starting point, if necessary conduct further research on data
compilers via the Internet.
The pro
SECTION 9: Exercises
9.1*
The SunTime Company, producers of fruit juice, wants to estimate the mean amount of orange
juice in the 64-ounce containers at a 99% confidence level. The company knows that the standard
deviation of amounts of orange juice in th
Rosewood Hotels & Resorts: Branding to Increase Customer Profitability and Lifetime Value
In the case study Rosewood Hotels & Resorts: Branding to Increase Customer Profitability and
Lifetime Value depicts a true understanding of how a company is trying t
SECTION 11: Exercises
11.1 You conduct a new scripting test versus your control script for inbound calls
coming from space advertising for the Liquid Face Lift product. The results of the test
and control panels are as shown below:
Assume the test script
SECTION 8: Exercises
8.1*
According to the Southern California Real Estate Association, the average sale price of homes in
Los Angeles was $208,922 in 2009 and $206,490 in 2008. Suppose that these means were based
on random samples of 420 Los Angeles home
Assessing a Companys Future Financial Health
Try to match the five following types of companies with their corresponding balance sheets and financial
ratios, which are shown in Exhibit 3.
1. Electric utility
Within exhibit 3 you can clearly see that the f
Supercrunchers Assignment
Questions Chapter 5
1. In Chapter 5, of Supercrunchers, "Experts versus Equations", the author makes a great case for the
fact that equations predict better than humans. What reasons does the author give that illustrate why a
hum
Sketch of the Solution : HW2
1. Prob 7.18 Find from the Normal table( Table 2 in appendix), satisfying Z1-/2 = 1. = 20.1587 = 0.3174 Therefore the the size of the confidence interval is 0.6826 2. Prob 7.26 (a) The unbiased estimate of the standard error o
Solution of homework #4
Chapter 7
Exercise 17.
d. The value z 1.04 cuts off the upper 15%(actually, 14.9%) of the standard normal distribution. e. The value z 0.84 cuts off the lower 20% of the distribution.
Chapter 8
Exercise2.
The reason the sample shou
MATH 408 SPRING 2010
QUIZ 2
A sample of size n = 100 is taken from a population that has a proportion p = 1/5. (Note: You may leave numerical answers in the form of fractions, but please simplify as much as possible.) a. Find such that P (|p - p| ) = 0.02
Stat 155 Fall 08 HW 1
Due date: 9/11/2008
Dont just write down the answer. Please show all steps. Grading scheme: 2 points for fully correct answer, 1 point for partially correct answer, 0 point for completely wrong answer. 1. Recall that the subtraction
Stat 155 Fall 08 Practice Final
December 9, 2008
Time: 3 hours. Please show all steps. 1. Consider a game of nim with inital conguration (48, 23, 74, 10) and with the restriction that at most three chips can be removed from a pile in a single move. Is thi