403 Chapter 8 Counting Techniques
Subdivide the given triangle into 4 equilateral triangles with side 1, as shown
in Figure 8.1. Since there are 5 points and only 4 small triangles, some pair of
points must lie in the same triangle. But it is easy to see

Advertisement-A Boon or Bane
A leaflet here and a banner there. Tarpaulins featuring famous people endorsing products loom
over the metropolitan streets. The television and radio scream brand new products and
technology, and mobile phone companies send yo

Fall 2016
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Fall 2016
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Fall 2016
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Fall 2016
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Fall 2016
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Fall 2016
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REPRESENTATION OF DATA
Graphical representation: Line plots
Graphical representation: Line plots
Outliers are data points whose values are
significantly larger or smaller than other
values, such as the ages of 30, and 58.
Clusters are isolated groups of

MODE
Mode
The mode in a list of numbers refers to the list of
numbers that occur most frequently
Examples: Find the mode of:
9, 3, 3, 44, 17 , 17, 44, 15, 15, 15, 27, 40, 8,
Put the numbers is order for ease:
3, 3, 8, 9, 15, 15, 15, 17, 17, 27, 40, 44,

BIOSTATISTICS
HISTORY
History of Statistics
Even though the term Statistics started
appearing in literature only in 18th century, the
practice of statistics was existent from time
immemorial
Census of all lands was conducted in Egypt
from 1400 BC
Simil

l
8.4 Arrangements and Selections with Repetitions 421
32. Prove by a combinatorial argument that rC(n, r) = nC(n ~ 1, r — l) for l 5 r 5 n.
33. Prove that C(n, m) - C(m, k) : C(n, k) - C(n — k, m - k) for k _<_ m 5 n by a combinatorial argument.
34. Prov

Math 184A: Fall 2013
Homework 1 Solutions
Due 5:00pm on Friday 10/4/2013
Problem 1: (Exercise 1.26 in Bna) We are given 17 points inside a regular triangle
o
of side length one. Prove that there are two points among them whose distance is not
more than 1/

Theorem 8.4
Example 8.5
Example 8.6
Example 8.7
8.2 Three Fundamental Principles 407
The Pigeonhole Principle If pigeons are placed into pigeonholes and there are
more pigeons than pigeonholes, then some

Introduction to Mendelian Genetics
The study of GENES and HEREDITY at
the phenotypic level has a long history.
People have long puzzled over
questions of inheritance
Questions about resemblance:
Why do children resemble their
parents?
How can disease

2.5 Mathematical ﬁtduction 77
The Principle of Mathematical Induction Let S(
the integer n. Suppose that, for some ﬁxed integer n
(1)7 5010) is true
(2) whenever k i
true.
n) be a statement involving
0: '
(that is, the statement is true if n = no) and
s a

INTRODUCTION TO IMMUNOLOGY
INNATE AND ADAPTIVE IMMUNITY
Tomar Ghansah, Ph.D.
Assistant Professor
MDC 3008
813-974-1825
Tghansah@health.usf.edu
RESOURCES
Immunology A Short Course
Fifth Edition
Richard Conic, Geoffrey Sunshine and Eli Benjamini
Cellular an

Challenge Questions for Unit 2 Genetics, Genes & Genomes
These questions are based on the concepts and principles presented in lecture and the
chapter material in the text. It is open resource, open book, but independent, original work
and answers. Use yo