Probability and Statistics course

Description

Welcome to Engineering Statistics and Probability Theory

This course will go over theories and implementation of engineering statistics and probability theories to real business problems. Each section has many examples, quizzes, and assessment exams.

Our course includes professional HD Videos with extensive case studies to show you how to apply this knowledge to solve real and practical problems.

In this course we will cover:

• Introduction to statistics and probability

• Why Study Statistics?

• Types of data

• Definitions: Populations, units, and Sample

• Generation of random number table

• The difference between Parameters & Statistics

• Branches of Statistics (Descriptive and Inferential statistics)

• Pareto chart

• Dot plot

• Scatter plot

• Frequency distribution

• Histogram

• Stem and Leaf display

• Measures of Central Tendency (Mean, Median, and Mode)

• Measures of Variation (Range, Variance and Standard Deviation)

• Weighted Mean

• Standard Deviation for Grouped Data

• Coefficient of variation

• Definitions (Probability experiment, Outcome, Sample space, and Event)

• Types of Probability

1. Classical (or theoretical) Probability

2. Empirical (or statistical) Probability

3. Subjective Probability

• Combining events

• Counting Principles

• Multiplication of choices

• Permutation

• Combination

• The Axioms of Probability

• Venn diagrams

• The Addition Rule

• Mutually Exclusive Events

• Conditional Probability

• The Multiplication Rule

• Independent Events

• Bayes’ Theorem

• Discrete Probability Distributions

• Types of Random Variables

• Discrete Probability Distributions (DPD)

• Binomial Distribution

• Hypergeometric Distribution

• Poisson Distribution

• Mean, Variance, and Standard Deviation of DPD

• Continuous Probability Distributions

• Normal Distribution

• The Standard Normal Distribution

• The Standard Normal Distribution Tables

• The Normal Approximation to the Binomial Distribution

• Sampling distributions

• Populations and Samples

• The Sampling Distribution of the Mean

• The Sampling Distribution of the Mean (σ Known) –> z-distribution

• The Sampling Distribution of the Mean (σ Unknown) –> t-distribution

• Sampling Distribution of the Variance –> χ2-distribution

• F - Distribution

• Estimation of Population’s

• Estimation of Population’s Mean

• Point Estimation

• Interval Estimation

• Normal (s known). Or n ³ 30

• Normal (s Unknown).

• Calculation of Sample Size

• Tests of Hypotheses

• Introduction to Hypothesis Testing

• Type I and type II errors

• Level of Significance

• Hypotheses Testing Process

• Test Statistic Selection

• Statistical Decision

• Hypothesis Testing for the Population’s Mean:

• Large Samples; n ≥ 30 or Normal population (σ Known) à (z)

• Small Samples: n < 30 and Normal population (σ Unknown) à (t)

• Tests of Hypotheses Using P-value

• Hypothesis Testing for Proportions

• Correlation and Regression

• Correlation Coefficient r

• scatter plot

• Correlation Coefficient

• Linear Regression

• Regression Line

• Linear combination of variables

• Covariance

• Correlation using covariance

• and much more!

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