University of California, Los Angeles
Department of Statistics
Statistics 100B Instructor: Nicolas Christou
Exam 1
03 February 2012
Name: 7
Problem 1 (25 points)
Answer the following questions: ‘
a. The pdf of a random variable X is f (:r) = dime—‘5'. W
University of California, Los Angeles
Department of Statistics
Statistics 100B
Instructor: Nicolas Christou
Exam 2 - practice questions
Problem 1
Answer the following questions:
2
a. Consider the regression model through the origin yi = 1 xi + i , for i =
University of California, Los Angeles
Department of Statistics
Statistics 100B Instructor: Nicolas Christou
Homework 3 — Solutions
EXERCISE 1
In the case when n : 2 the sample mean is X = Egg—{1 and therefore the sample variances2 is:
2 — X -x 2
s2 = zi—l
University of California, Los Angeles
Department of Statistics
Statistics 100B
Instructor: Nicolas Christou
Homework 1
EXERCISE 1
Find the distribution of the random variable X for each of the following moment-generating functions:
a. MX (t) =
1 t
3e
b. M
University of California, Los Angeles
Department of Statistics
Statistics 100B
Instructor: Nicolas Christou
The Central Limit Theorem
Suppose that a sample of size n is selected from a population that has mean and standard
deviation . Let X1 , X2 , , Xn b
University of California, Los Angeles
Department of Statistics
Statistics 100B Instructor: Nicolas Christou
Homework 4 — Solutions
EXERCISE 1
We know that X ~ b(n,p).
a. The likelihood function is L(p) = 1i‘(l — p)"’ and the log—likelihood lnL(p) = zlnp+
V University of California, Los Angeles
Department of Statistics
Statistics 100B Instructor: Nicolas Christou
Homework 1 - Solutions
EXERCISES 1
Find the distribution of the random variable X for each of the following moment-generating functions:
a. Mx(t)
Qi
University of California, Los Angeles
Department of Statistics
Statistics 1003 Instructor: Nicolas Christen
MMW‘SQQLU7TVW3
Problem 1 (25 points)
Answar the following questions:
Midterm exam
1'5 July 2014
a. Let X1,. . . ,Xk, . . . , Jim be independen
University of California, Los Angeles
Department of Statistics
Statistics 100B
Instructor: Nicolas Christou
Homework 7
EXERCISE 1
A coin is thrown independently 10 times to test that the probability of heads is
1
is not 2 . The test rejects H0 if either 0
University of California, Los Angeles
Department of Statistics
Instructor: Nicolas Christou
Statistics 100B
Homework 5
EXERCISE 1
Let X1 , X2 , , Xn be independent and identically distributed random variables from a Poisson distribution with parameter .
W
University of California, Los Angeles
Department of Statistics
Statistics 100B
Instructor: Nicolas Christou
Homework 8
EXERCISE 1
Answer the following questions:
a. The lifetime of certain batteries are supposed to have a variance of 150 hours2 . Using =
Chapter 04: Displaying and Summarizing
Quantitative Data
As before, it all starts with a pictureso lets look at some of the options when graphing
quantitative variables.
Graph Types
Histograms
Some people (mistakenly) use the terms bar chart and histogram
Chapter 20: Testing Hypotheses about Proportions
In the last chapter, we finally derived a way to estimate a parameter from a sample. Now, we
see how you can test whether or not a belief about a parameter value is supported by the data.
The Idea
So you fi
Chapter 23: Inferences About Means
Enough Proportions!
Weve spent the last two units working with proportions (or qualitative variables, at least)
now its time to turn our attentions to quantitative variables.
For qualitative variables, the parameter (whe
Chapter 06: The Standard Deviation as a Ruler and
the Normal Model
This is the worst chapter title ever! This chapter is about the most important random variable
distribution of them allthe normal distribution.
Measuring Position (again)
Earlier (several
Chapter 19: Confidence Intervals for Proportions
When we made our probability calculations back in chapter 18, we were holding on to one
last thing that kept us from reality: knowing the value of p. Since thats a parameter, we ought
not to know its value!
Chapter 18: Sampling Distribution Models
This is the last bit of theory before we get back to real-world methods.
Sampling Distributions: The Big Idea
Take a sample and summarize it with a statistic. Now take another samplewill you get the
same value for
Chapter 17: Probability Models
Now that we understand random variables, lets look at some of the more important ones.
Bernoulli Trials
but first, a concept: the Bernoulli Trial. A Bernoulli Trial is a random experiment where
the outcomes can be grouped in
Chapter 15: Probability Rules
OKtime to hunker down and put some detail on the work we started in the previous chapter.
Unions
The Union of two events contains all outcomes that belong to either event (and maybe both).
One nice way to think about the unio
Chapter 14: From Randomness to Probability
Types of Probability
There are actually three different types of probability. Subjective probability is probability
based on personal beliefs. Seriously! You hear people say these sort of things all the time
(esp
Chapter 21: More about Tests and Intervals
Thinking about p-values
It is important to remember that our conclusion at the end of a hypothesis test is based on a
conditional probabilitythe probability that we find is not the probability that the null
hypot
Chapter 16: Random Variables
So weve talked about variables. And weve talked about things that are random. Now its
time to put the two together.
The Idea
A Random Variable measures the (quantitative) result of some random experiment. Pick a
person at rand
Chapter 03: Displaying and Describing Categorical
Data
Frequency Tables
The first step in creating a graph for qualitative data is to create a frequency table. This is a
list of the values that were observed, and a count of how many times each was observe
Chapter 26: Comparing Counts (Chi Square)
Weve seen that you can turn a qualitative variable into a quantitative one (by counting the
number of successes and failures), but thats a compromiseit forces us into a very binary
existence. Life is so much more