Stat 330 (Fall 2015): Homework 5
Due: October 7, 2015
Show all of your work, and please staple your assignment if you use more than one sheet. Write your name,
the course number and the section on every sheet. Problems marked with * will be graded and one
Stat 330 (Fall 2015): Homework 3
Due: September 16, 2015
Show all of your work, and please staple your assignment if you use more than one sheet. Write your name,
the course number and the section on every sheet. Problems marked with * will be graded and
Stat 330 (Spring 2016): Homework 1
Due: 1/20/2016
Show all of your work, and please staple your assignment if you use more than one sheet. Write your name,
the course number and the section on every sheet. Problems marked with * will be graded and one add
Exercises 397
where you can mark which statistics youd like to obtain mean squared error 32, AN OVA
F~statistic, R2, Rgdj, etc.
You can also use stepwise (X , Y) to select variables for the multivariate regression. A window
opens such as on Figure 11.7, a
Stat 330 (Fall 2015): Homework 5
Due: October 7, 2015
Show all of your work, and please staple your assignment if you use more than one sheet. Write your name,
the course number and the section on every sheet. Problems marked with * will be graded and one
Stat 330 (Spring 2016): Homework 2
Due: January 27, 2016
Show all of your work, and please staple your assignment if you use more than one sheet. Write your name,
the course number and the section on every sheet. Problems marked with * will be graded and
Stat 330
Homework 9 Solution
Spring 2012
1. Cars arrive at a city ATM according to a Poisson process with average rate of 4 cars
every 15 minutes. The time each customer spends on bank transactions is Exponential
with the average time of 3 minutes. When a
68 Probability and Statistics for Computer Scientists
Exercises
3.1. A computer virus is trying to corrupt two les. The rst le will be corrupted with probability
0.4. Independently of it, the second le will be corrupted with probability 0.3.
(a) Compute
Stat 330
Homework 3 Solution
Spring 2012
1. Among 10 laptop computers, ve are good and ve have defects. Unaware of this, a
customer buys 6 laptops. What is the probability that exactly 2 laptops are defective
among them?
Solution: Here we assume that samp
Slide set 8
Stat 330 (Spring 2017)
Last update: January 31, 2017
Stat 330 (Spring 2017): slide set 8
Expected Value
Expectation For a discrete random variable X and a function h(), the
expected value of h(X) is defined as:
P
P
E[h(X)] xIm(X) h(x) pX (x) =
Slide set 4
Stat 330 (Spring 2017)
Last update: January 17, 2017
Stat 330 (Spring 2017): slide set 4
Unordered Samples Without Replacement
Experiment: A box has n items numbered 1, . . . , n. Select k n items
without replacement. (A number is drawn at mos
Slide set 2
Stat 330 (Spring 2017)
Last update: January 10, 2017
Stat 330 (Spring 2017): slide set 2
Probability
Example:
Consider the Event C (a successful transmission) defined earlier.
From our experience with the network provider, we can decide that t
Slide set 5
Stat 330 (Spring 2017)
Last update: January 19, 2017
Stat 330 (Spring 2017): slide set 5
Conditional Probability
Example 1: A box has 5 computer chips. Two are defective. Two chips are
selected from the box, one at a time.
1. Compute the proba
Slide set 9
Stat 330 (Spring 2017)
Last update: February 8, 2017
Stat 330 (Spring 2017): slide set 9
Important Discrete Distributions
Several distributions occur often enough to be worth exploring.
We will get to know the following distributions and their
Slide set 1
Stat 330 (Spring 2017)
Last update: January 9, 2017
Stat 330 (Spring 2017): slide set 1
Uncertainty/Randomness
There are many situations where, because we have limited knowledge
about a process, we cannot exactly describe its current state or
Slide set 2
Stat 330 (Spring 2017)
Last update: January 6, 2017
Stat 330 (Spring 2017): slide set 2
Probability
Example:
Consider the Event C (a successful transmission) defined earlier.
From our experience with the network provider, we can decide that th
Exam 3
Stat 330 Section B
14 December 2012 Name: k
Read all of the following information before starting the exam:
Read the questions carefully and completely. Answer each question and SHOW WORK in the
space provided. Partial credit will not be given if w
Stat 330: Exam II, March 14, 2014
Name: K9 \/ University ID#: [3315 6 73 A (1
point)
The total number of points that you can attempt to score is 44. The maximum score is: 40.
(i.6., If you score above 40 points, your score will be reported as 40 points:
Stat 330: Exam III, April 25, 2014
Name:
point)
The total number of points that you can attempt to score is 44. The maximum score is: 40.
Kay
University ID#: l Ll S 6 785]
(1
(216., If you score above 40 points, your score will be reported as 40 points: a
Slide set 6
Stat 330 (Spring 2017)
Last update: January 16, 2017
Stat 330 (Spring 2017): slide set 6
Total Probability Law and Bayes Rule
Experiment: Treasure Hunt
Box 1 has two gold coins
Box 2 has one gold coin and one silver.
Box 3 has two silver co
Slide set 1
Stat 330 (Spring 2017)
Last update: January 6, 2017
Stat 330 (Spring 2017): slide set 1
Uncertainty/Randomness
The lack of certainty, a state of having limited knowledge where it is
impossible to exactly describe current state or future outcom
Slide set 10
Stat 330 (Spring 2017)
Last update: February 13, 2017
Stat 330 (Spring 2017): slide set 10
Geometric distribution
Review: X =number of repetitions of the experiment until we have the first
success in a Bernoulli experiment.
1. The pmf is: pX
Slide set 7
Stat 330 (Spring 2017)
Last update: January 22, 2017
Stat 330 (Spring 2017): slide set 7
Random Variables
Intuitive idea: If the value of a numerical variable depends on the outcome
of an experiment, we call the variable a random variable.
Ran
Slide set 5
Stat 330 (Spring 2017)
Last update: January 16, 2017
Stat 330 (Spring 2017): slide set 5
Conditional Probability
Example 1: A box has 5 computer chips. Two are defective. Two chips are
selected from the box, one at a time.
1. Compute the proba
Slide set 4
Stat 330 (Fall 2015)
Last update: January 16, 2017
Stat 330 (Spring 2017): slide set 4
Unordered Samples Without Replacement
Experiment: A box has n items numbered 1, . . . , n. Select k n items
without replacement. (A number is drawn at most
Slide set 8
Stat 330 (Spring 2017)
Last update: January 22, 2017
Stat 330 (Spring 2017): slide set 8
Statistics of R.V.s
Expectation The expected value of a function h(X) is defined as
E[h(X)] := i h(xi) pX (xi).
The most important version of this is the
Slide set 3
Stat 330 (Spring 2017)
Last update: January 6, 2017
Stat 330 (Spring 2017): slide set 3
Example 1
A box contains 4 chips, 1 of them is defective. A person draws one chip at
random. What is a suitable probability that the person draws the defec
Slide set 6
Stat 330 (Spring 2017)
Last update: January 23, 2017
Stat 330 (Spring 2017): slide set 6
Total Probability Law and Bayes Rule
Experiment: Treasure Hunt
Box 1 has two gold coins
Box 2 has one gold coin and one silver.
Box 3 has two silver co
Stat 330 (Spring 2017): Homework 1
Due: January 18, 2017
Show all of your work, and please staple your assignment if you use more than one sheet. Write your name,
the course number and the section on every sheet. Problems marked with * will be graded and
Slide set 14
Stat 330 (Spring 2017)
Last update: February 5, 2017
Stat 330 (Spring 2017): slide set 14
Gamma Example (Baron 4.7)
Compilation of a computer program consists of 3 blocks that are processed
sequentially, one after the other. Each block takes
Slide set 16
Stat 330 (Spring 2017)
Last update: February 28, 2017
Stat 330 (Spring 2017): slide set 16
Stochastic Processes
A stochastic process is function of both time and experiment outcomes:
Xt() = X(t, ) for t T ,
where T is a set of possible time
Slide set 18
Stat 330 (Spring 2017)
Last update: March 8, 2017
Stat 330 (Spring 2017): slide set 18
Poisson Process
Consider a continuous-time stochastic process cfw_Xt, where at each time
t [0, ), Xt represents the number of hits on a webpage. This is a
Slide set 12
Stat 330 (Spring 2017)
Last update: February 16, 2017
Stat 330 (Spring 2017): slide set 12
Continuous Random Variables
All properties of discrete RVs have direct counterparts for continuous RVs.
One basic difference: Summations used in the ca