Stats 2D03
Short Answers to Test #1
# 1 (6 marks) Three fair dice (cubical) are thrown. What is the probability of the following
events? (Just write down the answers!)
(i) at least two of the numbers are even;
Answer = 1 , because this has the same probab
2014 Summer
STATS 2D03
Short answers to Test # 2
# 1. True or False Let X, Y be any two random variables. Then
(i) E[2X
Y 2 ] = 2E[X]
E[Y 2 ]
(ii) E[XY ] = E[X]E[Y ]
(iii)
E[X 2 ]
<
E[X]2 .
(iv) V ar(X + Y )
true
false
false
V ar(X) + V ar(Y ) false
# 2.
2014 Summer
Stats 2D03
Short Answers to Test #1
1. If you throw three fair dice what is the probability that:
(i) at least one of the numbers is even; answer: 1
(ii) they add up to 16; answer:
6
63
=
7
8
1
36
(iii) all three numbers are dierent. answer:
2
SUMMER 2014
STATISTICS 2D03E FINAL
QUESTIONS & SOLUTIONS
1) Let X be a random variable with probability density function
a) What is the value of c?
=1
b) What is the cumulative distribution function of X?
2) The lifetime of an electrical component has den
Randi Perriam
Assignment WebWork04 due 03/19/2016 at 01:07pm EDT
Problem 1. 1. (1 pt) Understand basic derivatives. Find y0 if
MATH1P97D03FW2015
Problem 6. 6. (1 pt) Evaluate the indefinite integral
3
y = x ln x
Z
Correct Answers:
3*x2 *ln(x) + x2
6ex dx
STATISTICS 2D03 - TEST 1
Dr. S. Asma
McMASTER UNIVERSITY,DayClass
DURATION OF EXAMINATION: 90 minutes
May 19, 2011
QUESTIONS & SOLUTIONS
1) a) 6 players are to be picked from a group of 14 seniors, 11 juniors, and 5 freshmen at
random. What is the probabi
The probability density function (PDF) P(x) of a continuous distribution is defined as the
derivative of the (cumulative) distribution function D(x),
D^'(x) =
[P(x)]_(-infty)^x
(1)
=
P(x)-P(-infty)
=
P(x),
=
P(X<=x)
=
int_(-infty)^xP(xi)dxi.
(2)
(3)
so
D(
The negative binomial distribution, also known as the Pascal distribution or Plya distribution,
gives the probability of r-1 successes and x failures in x+r-1 trials, and success on the (x+r)th
trial. The probability density function is therefore given by
The distribution function D(x), also called the cumulative distribution function (CDF) or
cumulative frequency function, describes the probability that a variate X takes on a value less
than or equal to a number x. The distribution function is sometimes a
A normal distribution in a variate X with mean mu and variance sigma^2 is a statistic distribution
with probability density function
P(x)=1/(sigmasqrt(2pi)e^(-(x-mu)^2/(2sigma^2)
(1)
on the domain x in (-infty,infty). While statisticians and mathematician
Given a Poisson process, the probability of obtaining exactly n successes in N trials is given by
the limit of a binomial distribution
P_p(n|N)=(N!)/(n!(N-n)!)p^n(1-p)^(N-n).
(1)
Viewing the distribution as a function of the expected number of successes
n
STATS 2D03, ASSIGNMENT # 4
(Due on November 18, 11:30am)
1, Suppose that we have a four-face dice. One face is red, one is blue and the
remaining two are black. Now we roll this dice 4 times independently. Let X and
Y be the number of red faces and blue f
Types of Distribution
A statistical distribution whose variables can take on only discrete values. Abramowitz and
Stegun (1972, p. 929) give a table of the parameters of most common discrete distributions.
A discrete distribution with probability function
STATS 2D03: Assignment 4
Due: Friday, November 18, 2016 by 1pm in the
lockers on the FIRST floor of Hamilton Hall
Please put the assignment in the appropriate locker
for your section, and your family name.
1. Each morning, a baker bakes a number of pies;
STATS 2D03: Assignment 3
Due: Monday, October 31, 2016 by 1pm in the
lockers on the FIRST floor of Hamilton Hall
Please put the assignment in the appropriate locker
for your section, and your family name.
1.[2] There are two coins. One is a regular coin,
Randi Perriam
Assignment WebWork04 due 03/19/2016 at 12:58pm EDT
MATH1P97D03FW2015
Problem 6. 6. (1 pt) Evaluate the indefinite integral:
Z
5
3
2
+ C.
8 x dx =
3
x
Problem 1. 1. (1 pt) Let
f (x) = 5 ln(4x)
f 0 (x) =
f 0 (3) =
Correct Answers:
Correct An
Randi Perriam
Assignment WebWork04 due 03/19/2016 at 12:55pm EDT
Problem 1. 1. (1 pt) Let
MATH1P97D03FW2015
Problem 7. 7. (1 pt) Find f if f 0 (x) = 12x3 + 10x + 4 and
f (1) = 2.
Answer: f (x) =
f (x) = 3 ln(5x)
f 0 (x) =
Correct Answers:
f 0 (5) =
3*x4+
Randi Perriam
Assignment WebWork04 due 03/19/2016 at 01:00pm EDT
MATH1P97D03FW2015
Problem 6. 6. (1 pt) Evaluate the indefinite integral:
Z
5
3
2
+ C.
8 x dx =
3
x
Problem 1. 1. (1 pt) Let
f (x) = 5 ln(4x)
f 0 (x) =
f 0 (3) =
Correct Answers:
Correct An
Mary Haj-Ahmad
Assignment WebWork04 due 03/21/2016 at 01:37pm EDT
Problem 1. 1. (1 pt) Understand basic derivatives. Find y0 if
MATH1P97D03FW2015
Problem 7. 7. (1 pt) Find f if f 0 (x) = 12x3 + 12x + 9 and
f (1) = 5.
Answer: f (x) =
4
y = x ln x
Correct A
Mary Haj-Ahmad
Assignment WebWork04 due 03/21/2016 at 01:38pm EDT
Problem 1. 1. (1 pt) Let
MATH1P97D03FW2015
Problem 7. 7. (1 pt) Find f if f 0 (x) = 12x3 + 12x + 7 and
f (1) = 1.
Answer: f (x) =
f (x) = 4 ln(6x)
f 0 (x) =
Correct Answers:
f 0 (4) =
3*x4
Josh Pigat
Assignment WebWork04 due 03/21/2016 at 12:52pm EDT
Problem 1. 1. (1 pt) Let
MATH1P97D03FW2015
Problem 6. 6. (1 pt) Evaluate the indefinite integral:
f (x) = 5 ln(7x)
Z
f 0 (x) =
4x2 + 5x 6 dx =
+ C.
f 0 (3) =
Correct Answers:
-5/x
-1.66666666
Player Name
Darwin Barney
Dioner Navarro
Edwin Encarnacion
Ezequiel Carrera
Jose Bautista
Josh Donaldson
Justin Smoak
Kevin Pillar
Melvin Upton Jr.
Michael Saunders
Russell Martin
Troy Tulowitzki
Returning player?
Bats left/right/switch
Stats2D03 - Fall 2016
Midterm Test 1 Information
Our first test will be the evening of MONDAY, OCTOBER 17
The test will last for 60 minutes. To find the room and time to which you have been
assigned, please look on the course web site on Avenue. The room
STATS 2D03: Assignment 5
Due: Thursday, December 8, 2016 by 1pm in the
lockers on the FIRST floor of Hamilton Hall
Please put the assignment in the appropriate locker
for your section, and your family name.
1. Suppose that the random variable X is normall
STATS 2D03
Short answers to Test # 2
# 1. True or False Let X, Y be any two random variables. Then
Y 2 ] = 2E[X]
(i) E[2X
E[Y 2 ]
(ii) E[XY ] = E[X]E[Y ]
(iii)
E[X 2 ]
<
E[X]2 .
false
false
V ar(X) + V ar(Y ) false
sh is
ar stu
ed d
vi y re
aC s
o
ou urc
STATS 2D03: Assignment 4
Due: Friday, November 18, 2016 by 1pm in the
lockers on the FIRST floor of Hamilton Hall
Please put the assignment in the appropriate locker
for your section, and your family name.
1. Each morning, a baker bakes a number of pies;
STATS 2D03: Test 2
McMaster University
Instructor: S. Feng and D. Lozinski
Date: November 21, 2016
Duration: 60 minutes.
Name:
Student ID Number:
Instructions:
This test paper is printed on both sides of the page.
There are 5 questions on pages 2 through
The geometric distribution is a discrete distribution for n=0, 1, 2, . having probability density
function
P(n)
=
p(1-p)^n
=
pq^n,
(1)
(2)
where 0<p<1, q=1-p, and distribution function is
D(n)
=
sum_(k=0)^(n)P(k)
=
1-q^(n+1).
(3)
(4)
The geometric distrib
Solutions of Assignment #2
1.
[0.25](a) P cfw_E F = P cfw_E + P cfw_F = 0.85.
[0.25](b) P cfw_EF c = P cfw_E = 0.25.
[0.25](c) P cfw_EF = 0.
[0.25](d) P cfw_(E F )c = 1 [P cfw_E + P cfw_F ] = 0.15.
2. Let W, T and D denote the events that a person is
STATS 2D03:
Solution of Test 1 - Early Version
McMaster University
Instructor: S. Feng and D. Lozinski
Date: October 17, 2016
Duration: 60 minutes.
1. [6 marks] An urn has 4 blue balls and 1 red ball. A ball is pulled at random, the
colour is noted, and t
STATS 2D03: Assignment 2
Due: Thursday, October 6, 2016 by 1pm in the
lockers on the FIRST floor of Hamilton Hall
Please put the assignment in the appropriate locker
for your section, and your family name.
1. Suppose that event E has a probability of P (E
STATS 2D03: Solutions of Test 1
McMaster University
Instructor: S. Feng and D. Lozinski
Date: October 17, 2016
Duration: 60 minutes.
1. [6 marks] A die is rolled 4 times. What is the probability that the number 5 comes
up exactly two times?
Answer:
4
2
1
Solutions of Assignment #1
1.[3]
(a) 7! = 5040.
(b) 2! 3! 4! = 288.
(c) 5! 3! = 720.
(d) 2! 3! 3! 2! = 144.
2. [1.5]
40
2
= 780.
3.[3]
Consider the following scenario: a committee of k is to be formed from
a group of p + q individuals with p people from