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
Statistics 265 Practice Midterm A 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 A 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 C 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 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
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 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 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
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 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 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 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 B 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
Stat 265 Chapter 2 Problems Mike Kowalski
Statistics 265 Chapter 2 Problems
1.
Four Card Game: Consider a game that consists of dealing out two hands of two cards from a deck of four cards. The
deck contains the Ace of Spades (AS), the Ace of Hearts (AH),
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, kowalski@ualb
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
Statistics 2013 Exercise book 4 Conditional Probability
Problem 1:
A bowl contains eight chips. Three of the chips are red and ve are blue. Four chips are
to be drawn successively at random and without replacement. Compute probability that
the colors alte
Stat 265 Chapter 2 Problem Answers Mike Kowalski
Statistics 265 Chapter 2 Problem Answers
DISCLAIMER: Some of these are abbreviated or final solutions. Its up to you to verify the answer.
1. Four Card Game: Consider a game that consists of dealing out two
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 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 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 am lit evenly. Let
X be the
STAT 265 - Chapter 5 Exam solutions
1. Let (X, Y) have joint density
f(x,y]=cfw_2 if0<x<1,0<y<1,0<x+y<1
0, elsewhere.
Calculate P(X < 1/2, Y < 1/2).
Solution: By geometry, the answeris 1/2. .13.,
P( xvi, Yc): 50 [3% WW
1
; o xlia
(l/ZJ/ZJ , :
,. I oi
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