Virtual University of Pakistan

Statistics and Probability STA301

Virtual University of Pakistan

i

STA301 – Statistics and Probability

TABLE OF CONTENTS

TITLE

LECTURE NO. 1

PAGE NO 1

Definition of Statistics Observation and Variable Types of Variables Measurement Sales Error of Measurement LECTURE NO. 2

6 16

Data collection Sampling

LECTURE NO. 3

Types of Data Tabulation and Presentation of Data Frequency distribution of Discrete variable LECTURE NO. 4

23 32 42

Frequency distribution of continuous variable

LECTURE NO. 5

Types o frequency Curves Cumulative frequency Distribution

LECTURE NO.

6

Stem and Leaf Introduction to Measures of Central Tendency Mode LECTURE NO. 7

53

Arithmetic Mean Weighted Mean Median in case of ungroup Data LECTURE NO.

8

62

Median in case of group Data Median in case of an open-ended frequency distribution Empirical relation between the mean, median and the mode Quantiles (quartiles, deciles & percentiles) Graphic location of Quantiles LECTURE NO.

9

70

Geometric mean Harmonic mean Relation between the arithmetic, geometric and harmonic means Some other measures of central tendency LECTURE NO. 10

76

Concept of dispersion Absolute and relative measures of dispersion Range Coefficient of dispersion Quartile deviation Coefficient of quartile deviation LECTURE NO. 11

82

Mean Deviation Standard Deviation and Variance Coefficient of variation LECTURE NO.

12

89

Chebychev’s Inequality The Empirical Rule The Five-Number Summary LECTURE NO. 13

95

Virtual University of Pakistan

ii

STA301 – Statistics and Probability

Box and Whisker Plot Pearson’s Coefficient of Skewness

LECTURE NO. 14

106

Bowley’s coefficient of Skewness The Concept of Kurtosis Percentile Coefficient of Kurtosis Moments & Moment Ratios Sheppard’s Corrections The Role of Moments in Describing Frequency Distributions LECTURE NO. 15

115

Simple Linear Regression Standard Error of Estimate Correlation LECTURE NO. 16

128

Basic Probability Theory Set Theory Counting Rules: The Rule of Multiplication LECTURE NO. 17

136

Permutations Combinations Random Experiment Sample Space Events Mutually Exclusive Events Exhaustive Events Equally Likely Events LECTURE NO. 18

143 147

Definitions of Probability Relative Frequency Definition of Probability LECTURE NO. 19

Relative Frequency Definition of Probability Axiomatic Definition of Probability Laws of Probability Rule of Complementation Addition Theorem LECTURE NO. 20

152

Application of Addition Theorem Conditional Probability Multiplication Theorem LECTURE NO. 21

156

Independent and Dependent Events Multiplication Theorem of Probability for Independent Events Marginal Probability LECTURE NO. 22

161

Bayes’ Theorem Discrete Random Variable Discrete Probability Distribution Graphical Representation of a Discrete Probability Distribution Mean, Standard Deviation and Coefficient of Variation of a Discrete Probability Distribution Distribution Function of a Discrete Random Variable LECTURE NO. 23

169

Graphical Representation of the Distribution Function of a Discrete Random Variable Mathematical Expectation Mean, Variance and Moments of a Discrete Probability Distribution Properties of Expected Values

LECTURE NO. 24

177

Virtual University of Pakistan

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STA301 – Statistics and Probability

Chebychev’s Inequality Concept of Continuous Probability Distribution Mathematical Expectation, Variance & Moments of a Continuous Probability Distribution LECTURE NO. 25

185

Mathematical Expectation, Variance & Moments of a Continuous Probability Distribution BIVARIATE Probability Distribution LECTURE NO. 26

192 199

BIVARIATE Probability Distributions (Discrete and Continuous) Properties of Expected Values in the case of Bivariate Probability Distributions LECTURE NO. 27

Properties of Expected...