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STATISTICS
Definitions
Statistics is the science of designing studies, gathering data, and then
classifying, summarizing, interpreting, and presenting these data to
supportthedecisionsthatareneeded.
Descriptive
MATHEMATICAL
EXPECTATION
MATHEMATICAL EXPECTATION
OBJECTIVES
the students are expected to:
solve for the mean and variance of a
random variable X.
relate the statistics to probability by
identifying the mean and variance as
connected to the probability.
M
Random Variables
MATH30-6
Probability and Statistics
SPECIFIC OBJECTIVES:
At the end of the lesson, the student is expected
to be able to:
Define a Random Variable
Differentiate a discrete from a continuous
random variable
Determine the probability distri
PROBABILITY
Concepts of Probability
MATH 30 Probability and Statistics
OBJECTIVES
At the end of this lesson, the students are
expected to :
1. compute for the probability of an event
2. identify various ways of solving for the
probability of an event.
PRO
Random Variables
MATH30-6
Probability and Statistics
SPECIFIC OBJECTIVES:
At the end of the lesson, the student is expected
to be able to:
Define a Random Variable
Differentiate a discrete from a continuous
random variable
Determine the probability distri
Conditional Probability
Conditional Probability
Is the probability that a certain event would
occur given a previous underlying event
already occur
Suppose the Mapua Mathematics Society
has 15 officers of whom 8 are seniors
and 7 are juniors. Among the se
1
Chapter 4
Mathematical Expectation
MEAN OF A RANDOM VARIABLE
The mean of the random variable X or the mean of the probability
distribution of X is the method of relative frequencies used to calculate the
average number of a random variable. The mean or
A random variable is a function that associates a real number with
each element in the sample space.
DISCRETE PROBABILITY DISTRIBUTION
The set of all ordered pairs (x,f(x) is a probability
distribution, probability function or probability mass function if
Some Continuous Probability Distributions
1. Continuous Uniform Distribution
One of the simplest continuous distributions in all statistics is
continuous uniform distribution. This is characterized by a density
function that is flat.
Definition: The densi
Stem-and-leaf Plot
- the distribution is presented in a combined tabular and graphic display.
Example p.21 Table 1.4 (walpole)
Table 1.4- car battery life (in years)
n=40
ex. 1.6, 1.9
STEM-AND-LEAF PLOT
Stem
1
2
3
4
Leaf
69
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0011112223334445567778899
1
CHAPTER II
PROBABILITY
2.1 Probability
Probability is a field of mathematics that deals with chance. We begin our discussion with a
few basic concepts and useful terminologies.
An experiment is an activity in which the results cannot be predicted with c
Example: A recent survey of a new cola reported the following percentages of people
who liked the taste. Find the weighted mean of the percentages
AREA
0avored No. surveyed
wx
1
40
1000
400
2
30
3000
900
3
50
800
400
w
x
1700
WM= SUM(wx)/SUM(w)
SUM(w)=
1.
Continuous Random Variable
MATH30-6
Probability and Statistics
SPECIFIC OBJECTIVES:
At the end of the lesson, the student is expected
to be able to:
Define the properties of Continuous Random Variable
Solve for the probability of a continuous Random
Varia
Discrete Random Variables
Binomial Distribution
Binomial Distribution
Examples
Example
Example
Poisson Distribution
Poisson Distribution
Examples
Examples
Examples
Continuous Random Variable
The Normal Distribution
The Normal Curve
The Normal Curve
The Normal Curve
The Normal Curve
The Normal Distribution
Chebyshevs Rule
For any positive constant 'k', the probability
that a random variable will take on a value
withi
STATISTICS
MATH 30-6
Probability and Statistics
OBJECTIVES
The students at the end of the lesson are expected
to:
Define statistics and its fields
Differentiate the fields of statistics and relate to
its significance
Determine the scientific procedures
TESTING OF HYPOTHESIS
MATH 30
Probability and Statistics
OBJECTIVES
At the end of the lesson the students are expected
to:
Define a statistical hypothesis
Create a Hypothesis from a given problem
Provide an alternative from the given hypothesis
Determine
Counting Techniques
MATH 30-6
Probability and Statistics
OBJECTIVES
At the end of this lesson, the students are
expected to :
Define Probability
Use Counting Techniques
Relate counting techniques to real life situations
PROBABILITY
Tool to relate the de
Ungrouped Data
MATH 30-6
Probability and Statistics
OBJECTIVES
The students at the end of the lesson are expected
to:
Define and Differentiate various measures of
describing data
Describe a given set of data using various
measures
Interpret values that
GROUPED DATA
MATH30-6
Probability and Statistics
OBJECTIVES
The students at the end of the lesson are expected
to:
Define and Differentiate various measures of
describing data
Describe a given set of data using various
measures
Interpret values that ar
ESTIMATION
MATH 30-6
Probability and Statistics
OBJECTIVES
The students at the end of the lesson are expected
to:
Define Estimation
Identify the different parameters and its sample
point estimation
List down the steps for interval estimation
Solve est
DATA PRESENTATIONS
MATH30-6
Probability and Statistics
OBJECTIVES
The students at the end of the lesson are expected
to:
Identify and learn various ways of presenting
data
Describe data through tables, graphs and charts
Describe and interpret data pres
1
STATISTICS
Definition: Statistics is a collection of methods for planning experiments,
obtaining data, and then analyzing, interpreting and drawing conclusions
based on the data.
Introduction: The term statistics has different meanings as either a plura
INTRODUCTION TO RANDOM VARIABLES
A random variable is a function that associates a real number with each
element in the sample space.
Discrete Random Variable
Example 1: The sample space giving a detailed description of each
possible outcome when 3 compon
CHAPTER 8
TYPES OF PROBABILITY DISTRIBUTIONS
8.1 Some Discrete Probability Distributions
The observations generated by different statistical experiments have the
same general type of behavior. These experiments encountered in practice can
be described by
1
CHAPTER 5
TYPES OF PROBABILITY DISTRIBUTIONS
Some Discrete Probability Distributions
The observations generated by different statistical experiments have the same
general type of behavior. These experiments encountered in practice can be described by
es