STAT4M03/6M03 Multivariate Statistics
Assignment 2
Due at 12:30pm on Monday, October 20, 2014
Instructions:
1. Ensure that your full name and student number are clearly marked on each page of your
solutions.
2. Start each question on a new page and clearl
A gamma distribution is a general type of statistical distribution that is related to
the beta distribution and arises naturally in processes for which the waiting times
between Poisson distributed events are relevant. Gamma distributions have two free
pa
Let there be n ways for a "good" selection and m ways for a "bad" selection out of a
total of n+m possibilities. Take N samples and let x_i equal 1 if selection i is
successful and 0 if it is not. Let x be the total number of successful selections,
x=sum_
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
The binomial distribution gives the discrete probability distribution P_p(n|N) of
obtaining exactly n successes out of N Bernoulli trials (where the result of each
Bernoulli trial is true with probability p and false with probability q=1-p). The
binomial
STAT4M03/6M03 Multivariate Statistics
Assignment 1
Due at 12:30pm on Monday, September 29, 2014
Instructions:
1. Ensure that your full name and student number are clearly marked on each page of your
solutions.
2. Start each question on a new page and clea
A general type of statistical distribution which is related to the gamma distribution.
Beta distributions have two free parameters, which are labeled according to one of
two notational conventions. The usual definition calls these alpha and beta, and the
STAT4M03/6M03 Multivariate Statistics
Assignment 4
Due at 12:30pm on Monday, December 1, 2014
Instructions:
1. Ensure that your full name and student number are clearly marked on each page of your
solutions.
2. Start each question on a new page and clearl
STAT4M03/6M03 Multivariate Statistics
Assignment 3
Due at 12:30pm on Monday, November 10, 2014
Instructions:
1. Ensure that your full name and student number are clearly marked on each page of your
solutions.
2. Start each question on a new page and clear
Given a Poisson distribution with rate of change lambda, the distribution of waiting
times between successive changes (with k=0) is
D(x)
=
P(X<=x)
=
1-P(X>x)
=
1-e^(-lambdax),
(1)
(2)
(3)
and the probability distribution function is
P(x)=D^'(x)=lambdae^(-
STATISTICS 4M03
Fall 2014
Dr. Angelo Canty
MIDTERM TEST
October 29, 2014.
DAY CLASS
DURATION OF EXAMINATION: 50 Minutes
THIS EXAMINATION PAPER INCLUDES 2 PAGES AND 3 QUESTIONS. YOU ARE RESPONSIBLE
FOR ENSURING THAT YOUR COPY OF THE PAPER IS COMPLETE. BRIN
STATISTICS 6M03
Fall 2014
Dr. Angelo Canty
MIDTERM TEST
October 29, 2014.
DAY CLASS
DURATION OF EXAMINATION: 50 Minutes
THIS EXAMINATION PAPER INCLUDES 2 PAGES AND 3 QUESTIONS. YOU ARE RESPONSIBLE
FOR ENSURING THAT YOUR COPY OF THE PAPER IS COMPLETE. BRIN
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(x