STAT 230, S15
Midterm 2
Practice Questions
Midterm 2 S14 questions
Question 1 (10 marks):
A free casino game has six envelopes each with cash amounts of 1, 2, 4, 8, 10, and 20 dollar(s).
You are randomly given an envelope and receive the cash.
a) (2) What
Stat 230 - Sample Questions - Midterm 1
1. Two sections of a statistics course are being taught. From what she has heard about the
two instructors, Melanie estimates that the chances of passing the course are 0.90 if she
gets Professor Chapin and 0.75 if
Quiz #1 Solution Stat 230: Probability (Winter 2014)
Question #1 (10 points):
The easiest way to do this is as follows: Instead of allocating the balls to the boxes, allocate the boxes
to the balls. For the rst part, well solve it for n boxes so that the
Course Outline
STAT 230: Probability (Winter 2014)
Dept. of Statistics & Actuarial Science, University of Waterloo
General Information
Instructors:
Section 002
Christian Boudreau, Ph.D.
Oce: M3 4217 Ext: 37321
E-mail: cboudreau@uwaterloo.ca
Section 001
Ja
STAT 340/CS 437 PROBLEM
SOLUTIONS.
1. 1.1 The following data gives the arrival times and the service times that each
customer will require for the rst 13 customers in a single server queue. On
arrival the customer either enters service if the server is fr
STAT 230
Tut 5, June 25th 2013
513
Question 1: A manufacturer of car radios ships them to retailers in cartons of n radios. The profit per
radio is $59.5, less shipping cost of $25 per carton, so the profit is ${59.5n-25) per carton. To promote
sales by
STAT 230
Tut 4
513
Question 1:
Computer system "crasheqs" at a large financial firm occur according to a Poisson Process with an
average of 21 per week.
a) Let X be the number of weeks with no crashes during a period of n weeks. Find the probability
fu
Stat 230
Tutorial 7
July 17th 2013
Question 1:
Two fair coins are tossed simultaneously. The first coin is tossed 3 times and the second coin is
g
tossed twice. Let X be the number of heads observed when tossing the first coin and Y the
number of head
18.440 Midterm 1, Spring 2011: 50 minutes, 100 points.
SOLUTIONS
1. (20 points) Consider an innite sequence of independent tosses of a coin
that comes up heads with probability p.
(a) Let X be such that the rst heads appears on the Xth toss. In other
word
Big-O Examples
Denition Let f and g be real-valued functions. We say that f (x) is O(g(x) if there are constants
C and k such that
|f (x)| C|g(x)| for all x > k.
Example 1 Show that f (x) = 4x2 5x + 3 is O(x2 ).
|f (x)| = |4x2 5x + 3|
|4x2 | + | 5x| + |3
DISCRETE MATH: LECTURE 13
DR. DANIEL FREEMAN
1. Chapter 5.4 Strong Mathematical Induction
Proving a statement by either mathematical induction or strong mathematical induction
is a two step process the rst step is called the basis step, the second step is
Gravitational Lensing Gravitational lensing, which is the deflection of light by gravitational fields and the resulting effect on images, is widely useful in cosmology and, at the same time, a source of irreducible uncertainty in certain measurements. Her
Week II:
REFLECTION AND REFRACTION AT SPHERICAL INTERFACES
II.A
Reflection and Focal Point of Concave Mirror (Report errors in measured quantities only)
Experiment: Place concave mirror into beam of parallel light rays, so that principal axis of mirror
co
Math 361, Problem set 11
Due 11/6/10
3
1. (3.4.32) Evaluate 2 exp(2(x 3)2 )dx - without a calculator. Use the
appendix table. Answer:
1
Note that if X has a N (3, 2 ) distribution then, X has pdf
2
fX (x) = exp(2(x 3)2 ),
2
< x <
Thus
3
2
exp(2(x3) )dx
A Collection of Dice Problems
with solutions and useful appendices
(a work continually in progress)
version January 12, 2015
Matthew M. Conroy
doctormatt at madandmoonly dot com
www.matthewconroy.com
A Collection of Dice Problems
Matthew M. Conroy
Thanks
Lecture 33
Wednesday 24th July 2013
Let X~N(5,4). An independent random variable
Y is also normal with a mean of 7 and a
standard deviation of 3. Find
a)
The probability that 2X differs from Y by more than 4.
b)
The minimum number of n independent X
obser
Stat 330, 56
[be 3.
ses and white roses, some of which have thorns and some do not. Let R be
et T be the event that a rose has thorns. it is known that 1A of the roses
ave thorns, 3/7 of roses with thorns are white. When selecting a rose
T,R 07,}? nT,an
Lecture 8
27th May 2013
Tree diagrams
These are useful in giving a visual
representation of conditional probabilities.
The tree diagram consists of Nodes and
Branches.
Each branch represents a particular path
that could be followed.
Example: A fair c
Lecture 11
3rd June 2013
Binomial Distribution:
Physical setup:
Suppose an experiment has two possible
outcomes, success and failure.
The P(Success)=p and hence, the
P(Failure)=1-p
Repeat the experiment n independent
times.
Let X be the number of succes
Lecture 9
29th May 2013
X
Discrete
R.V.
Range consists of
a finite or countably
infinite set of values.
The random variable
can take integer
values or, in general,
values in a countable
set, e.g. 0,1,2,.
Continuous
R.V.
Examples
Discrete r.vs
Continuous
Lecture 24
3rd July 2013
A potter is producing teapots one at a
time. Assume that they are produced
independently of each other and with
probability p the pot will be satisfactory;
the rest are sold at a lower price. The
number, X, of rejects produced be
Lecture 25
5th July 2013
Interpretation of Covariance
X=persons height and Y=persons weight,
these two r.vs will have positive
covariance
Cov(X, Y)>0
X=thickness of the attic insulation in a
house and Y=heating cost of the house.
Here
Cov(X, Y) <0.
Lecture 26
8th July 2013
Example: We have N letters to N different
people, and N envelopes addressed to
those N people. One letter is put in each
envelope at random. Find the mean and
variance of the number of letters placed in
the right envelope.
Lecture 28
12th July 2013
Mean:
Variance:
Exponential Distribution:
Physical setup: In a Poisson Process for
events in time let X: length of time we wait
until the first occurrence. Then X has an
exponential distribution.
Example:
If phone calls to a
Lecture 31
19th July 2013
Example:
Let X~N(3, 25)
Find
a)P(X<2)
b)P(X>5)
c)Find a number c such that P(X>c)=0.95
Examples: Let X~N(3, 5) and Y~N(6, 14)
be independent. Find P(X>Y)
I will be away from July 20th up to and
including August 5th.
I will
EMERIS INC. (EMI)
Business Description
Emeris Inc. (Emeris, EMI) was formed in 1992 through a spinoff of the regulated utility operations
controlled at the time by the Nova Scotia provincial government. Originally, the company only owned
assets in the pro
MODEL OVERVIEW
The valuation model used to determine the fair price of the securities revolves around a discounted cash
flow (DCF) model that discounts the future unlevered free cash flows (UFCF) / free cash flows to firm
(FCFF) at a calculated weighted a
Revenue Schedule - EMI
Year 0
Year 1
Year 2
Year 3
Year 4
Year 5
Rate Base
Net fixed assets
7,300.00
7,617.06
7,840.35
8,069.64
8,305.19
8,499.97
Allowed rate of return
1,084.05
1,131.13
1,164.29
1,198.34
1,233.32
1,262.24
1,084.05
1,131.13
1,164.29
1,198