STAT 265 Assignment 3
Due Thursday November 3
Suppose that Y has density function f(y) = ky2 (1 y) 1(0,1) (y).
1.
(a)
Find the value of k that makes f a probability density function.
(b)
Work out the formula for the cumulative distribution function F.
Sup
STAT 265 - Chapter 2 Exam solutions
1. The sample space is S = cfw_a, b, c, d, e. If P(a) = P(b) = .15, P(c) = .40, and P(d) =
2P(e) nd the probabilities P(d) and P(e).
Solution: From the given information we have
1 = .15 + .15 + .40 + 2P(e) + P(e) = .70
STAT 265 Assignment 5 solutions
1. Wires manufactured for use in a computer system are specied to have resistance
between .12 and .14 ohms. Due to random error, the actual resistance is a normal random
variable with mean = .13 ohm and = .005 ohm.
(a) What
STAT 265 Assignment 4 solutions
The density function f for the random variable Y has the form f(y) = cy2 (1y) 1(0,1) (y).
1.
(a) Calculate the value c.
(b) Find P(1/4 < Y < 3/4).
Solution:
(a)
(b)
1
0
y2 (1 y) dy = 1/12 so that c = 12.
P(1/4 < Y < 3/4) =
STAT 265, Section A1 Final Exam
Instructor: B. Schmuland
When: Tuesday December 13, 2 pm 5 pm
Where: Universiade Pavilion (aka Butterdome)
I will hold drop-in office hours in my office (CAB
473) on Monday December 12 from 9am to 5pm,
and Tuesday December
Statistics 265 Practice Midterm E Mike Kowalski
University of Alberta
Department of Mathematical and Statistical Sciences
Instructions: This is a closed book exam. Only the formula sheet provided and a calculator are allowed in
the exam. Time: 80 minutes
Statistics 265 Practice Midterm F Mike Kowalski
University of Alberta
Department of Mathematical and Statistical Sciences
Instructions: This is a closed book exam. Only the formula sheet provided and a calculator are allowed in
the exam. Time: 80 minutes
Statistics 265 Practice Midterm B Mike Kowalski
University of Alberta
Department of Mathematical and Statistical Sciences
Instructions: This is a closed book exam. Only the formula sheet provided and a calculator are allowed in the
exam. Time: 80 minutes
Statistics 265 Practice Midterm D Mike Kowalski
University of Alberta
Department of Mathematical and Statistical Sciences
Instructions: This is a closed book exam. Only the formula sheet provided and a calculator are
allowed in the exam. Time: 80 minutes
STAT 265 - Chapter 3 Exam solutions
1. Suppose that two equally matched teams play a best-of-seven series. What is the
chance that the series will need a seventh game?
Solution: The seventh game is needed exactly when the rst six games split evenly. Let
X
STAT 265 Assignment 1 solutions
1. Let S be the set of all integers and let A, B, C, D be all multiples of 2, 3, 4, 5 respectively.
Dene E = A (B (C D). How many positive integers in E are less than 100?
Solution: The brute force solution lists all the nu
STAT 265 - Chapter 4 Exam solutions
1. A juice bottle machine lls 16 ounce bottles. The actual amount dispensed is approximately normal with mean = 15 ounces and = 1 ounce. What proportion of bottles
will overow?
Solution: If Y is the amount dispensed, th
STAT 265 Assignment 2 solutions
1. Suppose that you deal out all 52 cards from an ordinary deck without replacement.
Let A be the event that the rst card is red, and B be the event that the last card is black.
Are A and B independent events? Justify.
Solu
STAT 265 Assignment 3 solutions
1. A certain fairground game costs one dollar to play. You get to roll three dice, and if
there are any sixes you get back your dollar plus as many dollars as there are sixes. If
there are no sixes you lose your dollar.
Wha
Stat 265 Final Exam Practice Questions
Example 1 : Consider a two-stage game described as follows:
Stage 1: Generate a Uniform(0,1) random number, Q. Q ~ Uniform(0,1)
Stage 2: Repeat n iid Bernoulli(q) trials, where q is the value generated in Step 1.
Let
Stat 265 Final Exam Practice Questions
Example 1 :
Consider a two-stage game described as follows:
Stage 1: Generate a Uniform(0,1) random number, Q.
Q ~ Uniform(0,1)
Stage 2: Repeat n iid Bernoulli(q) trials, where q is the value
generated in Step 1.
Le
848 Appendix 3
Tables
Table 4 Normal Curve Areas
Standard normal probability in right-hand tail
(for negative values of 2, areas are found by symmetry)
Second decimal place of z
z .00 .01 .02 .03 .04 .05 .06 .07 .08 .09
0.0 .5000 .4960 .4920 .4880 .48
Statistics 265 Practice Midterm D Sol Mike Kowalski
University of Alberta
Department of Mathematical and Statistical Sciences
Instructions: This is a closed book exam. Only the formula sheet provided and a calculator are
allowed in the exam. Time: 80 minu
Statistics 265 Practice Midterm C Sol Mike Kowalski
University of Alberta
Department of Mathematical and Statistical Sciences
Instructions: This is a closed book exam. Only the formula sheet provided and a calculator are allowed in
the exam. Time: 80 minu
Statistics 265 Practice Midterm E Sol Mike Kowalski
University of Alberta
Department of Mathematical and Statistical Sciences
Instructions: This is a closed book exam. Only the formula sheet provided and a calculator are allowed in
the exam. Time: 80 minu
Bivariate Normal Density
Let X and Y be independent standard normal random
variables. Theirjoint
density, written as a function of
x
1
the vector x =
, is f(x, y) =
exp(xT x/2).
2
y
1
For any 1 < < 1, the matrix =
is
1
symmetric and positive definite,
A multinomial experiment possesses the following properties:
1. The experiment consists of n identical trials.
2. The outcome of each trial falls into one of k classes or cells.
3. The probability that the outcome of a single trial falls into
cell i is pi
Math 2030 3.00 Page 1
Midterm test May 20, 2010
1. (25 POINTS) Suppose that P(A) : 0.15, P(B) : 0.2 and P(C’) = 0.35. Moreover, events
A and B are mutually exclusive. Events A and C' are independent and the events B and C'
are also independent.
(a) (5 P
Philadelphia University
Department of Basic Sciences and Mathematics
First Exam
Probability Theory
1-4-2014
1. (3 points) How many subsets of size 4 of the set S = cfw_1, 2, , 20 contain at least one of
the elements 1, 2, 3, 4, 5?
!
!
20
20 5
Solution:
1
Probability and Statistics
Dr. John Harris
October , 200_
2.8 The Two Laws of Probability
a) The Multiplicative Law
b) The Additive Law
Theorem 2.5: (Multiplicative Law or Intersection). Given two events A and B
P(A B) = P(A and B)
= P(A) * P(B| A).
If
Sequences and Series
You have probably learned about Taylor polynomials and, in particular, that
ex = 1 + x +
xn
x2 x3
+
+
+ En (x)
2!
3!
n!
where En (x) is the error introduced when you approximate ex by its Taylor polynomial of
degree n. You may have ev
Statistics 265 Course Outline Spring 2015 Mike Kowalski
STATISTICS 265 STATISTICS I Fall 2015
University of Alberta Department of Mathematical and Statistical Sciences
https:/eclass.srv.ualberta.ca/portal/
Instructor:
Mike Kowalski, CAB 487, [email protected]
Statistics 265 Chapter 1 and 2 Notes Probability Mike Kowalski
Stat 265 (Statistics I) Calendar Description:
Sample space, events, combinatorial probability, conditional
probability, independent events, Bayes Theorem, random
variables, discrete random var
Stat 265 Midterm Exam Information:
70 minute exam held Friday, May 26 during class time.
Closed book. The formula sheets will be provided.
Only non-programmable / non-graphing calculators are acceptable.
Format: 6 question worth 10 marks each. The exa
Stat 265: Chapters 2 5
Chapter 2: Introduction to Probability
2.1 2.2: What is Probability?
2.3 2.4: Probability Model (Discrete)
Review of basic set notation and set relations
Review of basic probability rules
2.5 2.6: Calculating Probability I The Sampl
Statistics 265 Midterm Spring 2017 Mike Kowalski
University of Alberta
Department of Mathematical and Statistical Sciences
Instructions: This is a closed book exam. Only the formula sheet provided and a nonprogrammable/graphing calculator are allowed in t
Chapter 3 Problem 15: Small electrical motors are shipped in lots of 50. Before such a shipment is accepted
an inspector chooses 5 motors at random and tests them. If none of the motors are found to be defective,
the shipment is accepted. If one or more a
Stat 265 Practice Final 3 Mike Kowalski
University of Alberta
Department of Mathematical and Statistical Sciences
Stat 265 Practice Final Exam 3
Instructor: Mike Kowalski
Instructions: This is a closed book exam. Only the formula sheet provided and a calc