Midterm Exam 1 Review
You can bring a doublesided cheating sheet and a calculator with you in the exam. The exam will consist of multiple choices and written problems. Please go through all examples discussed in class and the homework problems. S
CMPSC 121 Fall 2015 Assignment 5
Using the code given in class as a base, write functions to move
each of the chess pieces. Do them in the following order to
maximize your grade:
Piece
Rook
Bishop
Queen
King
Knight
Pawn
% grade
20%
20%
20%
20%
10%
10%
You
Lesson 9: Moment Generating
Functions
Recall the mean and the variance of a random variable X:
Likewise, for any positive integer r
! =
! ()
!
Lets define a function that generates moments of a distribution.
Moment Generating Function (MGF)
Definition:
Lesson 5: Independent Events
Two events are said to be independent if occurrence of one event has no
effect on the chance of occurrence of the other event.
Example: Me going grocery shopping today has nothing to do with what one
of your guys had for break
Lesson 6: Bayes Theorem
Little bit of History!
Rev. Thomas Bayes (17011761) gave us a way to find the conditional probability of
an event P(A  B), when the "reverse" conditional probability P(B  A) is the
probability that is known. Need P(A), P(B)>0.
B
Lesson 2: Probability Rules and
Properties
Probability
Probability interpretation in long run
Suppose I toss a fair coin in which the probability of observing a head is 0.5
and the probability of observing a tail is 0.5.
What if I toss the coin 3 times? I
Lesson 4: Conditional Probability
The probability we assign to an event can change if we know that some other
event has already occurred.
Consider two events A and B. If I tell you that event B has already occurred
condition probability ask you what is th
Lecture 1 Chapter 1
Monday, August 25th
Introduction
What is Statistics?
Where do we use Statistics?
Definitions
Data is a collection of facts Population is a well defined collection of objects that are of interest When we have available information for a
Lecture 2 Chapter 1
Wednesday, August 27th
StemandLeaf Diagram
Steps:
Select the stem values List stem values in a vertical column Record the leaf for every observation next to the corresponding stem value Write the key
Example
I ask 20 professors in th
Lecture 3 Chapter 1
Friday, August 29th
Measures
What might be interesting features of the data that we might want to know about?
Measures
In this class we will learn two categories of measures:
Measures of location
Mean Median Trimmed mean Percentiles
Me
Lecture 4 Chapter 1
Wednesday, September 3rd
Measures of variability
Range is the range of values Formula:
Range = maximum minimum
Example: I give a test in a class and I take a sample of 6 students. The grades are: 50, 70, 64, 94, 78, 88. Find the range
Lesson 3: Methods of Enumeration
So far we learned about random events associated with simple experiments
and calculating their probabilities.
Here, we will learn about counting techniques that are useful in determining
the number of outcomes associated w
Lesson 11: Geometric and Negative
Binomial Distributions
Geometric Distribution
We know the distribution of X, if X is the number of success occurred in n
independent Bernoulli trails.
Example: Toss a fair coin 10 times and X is the number of heads occurr
Lesson 3: Methods of Enumeration
So far we learned about random events associated with simple experiments
and calculating their probabilities.
Here, we will learn about counting techniques that are useful in determining
the number of outcomes associated w
Lesson 4: Conditional Probability
The probability we assign to an event can change if we know that some other
event has already occurred.
Consider two events A and B. If I tell you that event B has already occurred
condition probability ask you what is th
Lesson 2: Probability Rules and
Properties
Probability
us
gives
Consider
then
idea about
an
event
an
PCA)
=
A
NCAT
N (5)
how
likely
defined
on
Total
#
of
for
unpredictable
an
He
sample space
#
of
ways
ways
5
can
A
is
can
event
to happen
'
happen
d
happen
Lesson 6: Bayes Theorem
Little bit of History!
Rev. Thomas Bayes (17011761) gave us a way to find the conditional probability of
an event P(A  B), when the "reverse" conditional probability P(B  A) is the
probability that is known. Need P(A), P(B)>0.
B
Lesson 5: Independent Events
Two events are said to be independent if occurrence of one event has no
effect on the chance of occurrence of the other event.
Example: Me going grocery shopping today has nothing to do with what one
of your guys had for break
Stat 318 Midterm #2
Fall 2015, Section 2
November 13th, 2015
Student Name:
Student ID:
1. You must show all of your work in order to receive full and/or partial credit. No
work=No Credit.
2. You have 50 minutes in total. No additional time will be given.
Lesson 10: Binomial Distribution
First we will see what is a Bernoulli random variable.
Bernoulli Distribution
Consider a random experiment with only two possible outcomes.
Examples: Heads or tails
Success or failure
Defective or nondefective
This is wha
Lesson 7: Discrete Random Variables
From lesson 1 through lesson 6 we talked about basic probability rules and
some counting techniques that help us determine the probabilities associated
with more complicated experiments.
In the next few lessons we will
Lesson 8: Mathematical Expectations
We talked about what is a probability distribution in the previous lesson. Now we are
going discuss about finding expected values so that we can summarize important
characteristics of probability distributions.
Example:
Lecture 5 Chapter 2
Monday, September 8th
Probability
What is probability? Probability refers to the study of uncertainty and randomness
Definitions
Experiment is any process whose outcome is subject to uncertainty. Sample space of an experiment is the se
Lecture 6 Chapter 2
Wednesday, September 10th
Probability
The objective of probability is to assign to each event A, a number P(A), which is called probability of the event A and will give a precise measure of the chance that A will occur.
Axiom of Probab
Lecture 18 Chapter 4
Monday, October 27th
Expected value
The expected value of a continuous random variable X with pdf f(x) is
x = E ( X ) =

xf ( x ) dx
Example 4.10 page 168
Properties of expected value
If X is a continuous random variable with pdf f(
Lecture 19 Chapter 4
Wednesday, October 29th
Normal distribution
"Normal distribution is a statistical unicorn" It is the most important distribution in statistics. Most of the random variables out in nature fit naturally to normal distribution Of course,
Lecture 20 Chapter 4
Monday, November 3rd
Gamma function
In this lecture we will use a lot the gamma function. For > 0 the gamma function is defined as follows: 1  x ( ) = x e dx
0
Properties of gamma function: ( ) = (  1) (  1) For integer n, ( n ) =
Lecture 21 Chapter 4
Wednesday, November 5th
This Lecture
We will talk what happens when we know the pdf of a random variable and then we want to learn the pdf of another variable. There is only one theorem in this section. If the conditions in each case
Quiz #7 Friday, October 19th
NAME: _ Grade: _ out of 25. You have 30 minutes to complete this Quiz. This Quiz is a closed book and Notes exam. You may use the Tables I have distributed in class, though. Exercises 3 and 4 are on the reverse side. Exe
Quiz #6 Friday, October 12th
NAME: _ Grade: _ out of 25. You have 20 minutes to complete this Quiz. This Quiz is a closed book and Notes exam Exercise 1: (30 points) Let say that the probability that someone will fail X number of classes during the