Counting Techniques
Fundamental Counting Principle
In a sequence of events, the total possible number of ways all events can performed is the product of the
possible number of ways each individual event can be performed.
The Bluman text calls this multipl
MAT 2379, Introduction to biostatistics, Final Exam Study Guide
1
There will be 25 questions in the nal. The formula sheet will be given
to you, together with normal, t and 2 tables.
This is not a nal version of this le!
Resources:
Final Exam Formula She
MAT 2379, Introduction to biostatistics, Assignment 4
1
MAT 2379, Introduction to biostatistics
Solution to Assignment 4
Due date: Friday November 15, 2013
T otal = 100 marks
Problem 1. (a) The sample mean is
x=
1
(4.2 + 4.6 + . . . + 5.8) = 4.68
12
The s
MAT 2379 - Spring 2011
Assignment 2 : Solutions
3.27 (5 points) This question deals with the binomial distribution with
parameters n = 4, p = 0.42
(a) P (Y = 0) =4 C0 (0.42)0 (1 0.42)4 = 0.1132
(b) P (Y = 1) =4 C1 (0.42)1 (1 0.42)3 = 0.3278
(c) P (Y = 2)
MAT 2379 - Spring 2011
Assignment 3 : Solutions
4.1 (3 points) This question deals with the normal distribution with mean
0,variance 1
(a) P (1.5 Z 1.5) =0.9332 0.0668 = 0.866 4
(b) P (2.5 Z ) = 1 0.9938 = 0.006 2
(c) P ( |Z | 3.5) = 2P (Z 3.5) = 2(0.0013
MAT 2379 - Spring 2011
Assignment 4 : Solutions
5.3 (3 points) This question deals with the binomial distribution with
n = 5, p = 0.39. From Table 3.7, P (Y = y ) = n py (1 p)ny , y = 0, 1, ., n
y
a) (i) P (Y = 0) =0.08
(ii) P (Y = 1) =0.27
(iii) P (Y = 2
MAT 2379 - Spring 2011
Assignment 7 : Solutions
8.21 (2 points) P lan II is better because we want that the units within
a block to be more nearly alike. Under Plan I the eect of rain would be
confounded with the varieties.
8.38 (3 points) a) This should
MAT 2379 - Spring 2011
Assignment 5 : Solutions
6.12 (3 points)
5898
a) y = 28.7, s = 4.5898, SE = 4.6 = 1. 873 8
Condence interval 28.7 2.571 (1. 873 8)
(23.8, 33.6)
b) T he mean blood serum concentration of Gentamicin in healthy threeold female Suolk sh
MAT 2379
Introduction to biostatistics
Summary of R commands (Part 1)
1. Binomial distribution with parameters n and p:
To compute f (x) = P (X = x) :
dbinom(x,n,p)
To compute F (x) = P (X x) :
pbinom(x,n,p)
2. Normal law with parameters = mu and = sigma:
MAT 2379
Introduction to biostatistics
Summary of R commands (Part 2): Sections 9.2
1. To generate a sample of size n from a binomial distribution with m trials and probability of
success p: (this procedure is called sampling from the binomial distributio
MAT 2379
Introduction to biostatistics
Summary of R commands (Part 3): Sections 9.3
1. To arrange in increasing order the values in a variable x (and store the values in a variable y ):
y=sort(x)
2. To calculate the relative orders for a sample of size n,
MAT 2379
Introduction to biostatistics
Summary of R commands (Part 5): Chapters 12-13
Chapter 12. Assume that the data for the two populations are saved in variables x1 and x2. For
example,
x1=c(46.1,37.7,54.2,44.7,30.9,38.5,38.0,55.0)
x2=c(49.8,51.5,50.7
MAT 2379
Introduction to biostatistics
Summary of R commands (Part 4): Chapters 10-11
Condence Intervals (Chapter 10)
1. To produce a 95% condence interval for the mean when 2 is unknown:
t.test(x)$conf.int
2. To produce a 98% condence interval for the me
MAT 2379 : Fall 2013
The table below links the questions from the online bank of questions to the
chapters in the textbook.
Sections from
the textbook
Chapter 1
Section 2.1
Section 2.2
Chapter 3
Chapter 4
Chapter 5
Section 6.1
Section 6.2
Section 7.2
Sect
Vector Equation of a Straight Line
The cartesian equation for a straight line is y = mx + c, where m represents the gradient of the line, and c is the
point where the line crosses the y-axis.
A vector equation for a line similarly needs 2 pieces of inform