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Fall 2013 Course Outline
Stat 206 - Statistics for Software Engineers
University of Waterloo
Instructor: William Marshall,
M3-4128
x31528
(wjmarsha@uwaterloo.ca)
Lecture/Tutorial Location and Times:
Lectures: M/W/F 12:30 - 1:20, MC1085
Tutorial: Th 1:00
Stat 206
Exam Practice Problems
1. There are 6 passengers on the bus, and there are 6 remaining stops before the end of
the route. Assuming passengers get o randomly and independently, and that every
passenger must get o the bus by the end, what is the pr
Fall 2013
Stat 206 - Midterm II
Test Information
Date: Thursday November 14th
Time: 1:00 - 1:50 pm
Room: MC2066
You may bring a non-programmable calculator
No study sheet, or other aids
Content
Continuous Probability Distributions
Uniform distribut
Probability Rules
Formula
P
P (A) = i P (A|Bi )P (Bi )
Law of Total Probability
Bayes Theorem
P (B|A) =
Distribution
PDF f(x)
Binomial(n,p)
f (x) =
P (A|B)P (B)
P (A|B)P (B)+P (A|B )P (B )
n
x
Expected Value
px (1
x
p)n
x
Geometric(p)
1
p
(1 p)
p2
nr
N
rn
Normal
Distribution
Normal Distribution
October 23, 2013
Normal Distribution
Normal
Distribution
A random variable X has a normal distribution, denoted
X N(, 2 ), if the pdf has the form
f (x) = p
1
2
2
E (X ) = ,
e
1
2
(x
2
),
Var (X ) =
x 2R
2
Example
Sampling
distribution
Sampling distribution
October 28, 2013
Statistical Inference
Sampling
distribution
The goal of statistical inference is to draw conclusions
about a population
To do this, we select a subset of the population, the
sample and measure t
Probability
Probability
What is Probability?
Probability
Probability measures the uncertainty associated with an
experiment
Three denitions of probability,
1
Classical
Number of ways an event can occur
Total number of equally likely outcomes
2
3
Relative
Binomial CI
Condence
Intervals I
Consider an i.i.d sample of size n, with Xi Bernoulli(p)
Alternatively, a single sample from a X Binomial(n, p)
Estimate the probability of a success
p=
X
n
Pivotal Quantity: Using Binomial approximation, if n > 5
p
and n(
Data Types
Introduction
Categorical variable: A qualitative measure. Each unit
belongs to one of K possible classes (levels, categories).
Discrete variable: A quantitative measure. Each units
measurement can take on one of a countable number of
possible v
Condence
Intervals II
Condence Intervals II
November 4, 2013
Condence Intervals for Two Means
Condence
Intervals II
More applications than CIs for a single mean
Two types:
Exact CI for paired (dependent) observations
Approximate CI for independent observa
Fall 2013
Stat 206 - Exam
Exam Information
Date: Thursday December 12th
Time: 9:00 - 11:30 am
Room: DC1351
You may bring a non-programmable calculator
Formula Sheet and Tables (on learn) will be provided for you
Review Material
Midterm I practice pr
Stat 206
Midterm II Practice Problems
p
1. Let X be a continuous random variable with probability function f (x) = k x, R(X) =
(0, 4/9)
(a) Find k such that f(x) is a true probability function
(b) Find the probability that X is less than 1/4
(c) What is t
Stat 206
Midterm II Solutions
p
1. Let X be a continuous random variable with probability function f (x) = k x, R(X) =
(0, 4/9)
(a) Find k such that f(x) is a true probability function
(b) Find the probability that X is less than 1/4
(c) What is the media
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Condence
Intervals I
Condence Intervals I
October 30, 2013
Point Estimation
Condence
Intervals I
Consider a random sample of size n,
cfw_X1 , X2 , X3 , ., Xn
A probability model is selected which is appropriate for the
experiment
The probability function