MODULE 3: PROBABILITY THEORY AND DISTRIBUTIONS

MODULE 3: PROBABILITY THEORY AND DISTRIBUTIONS

By: ENGR. FRANZ JOHANN DE VERA, ENGRD.

Introduction to Probability Theory

Probability is the measure of uncertainty of events occurring.

• Essential in engineering for decision-making under uncertainty.

• Basic concepts include:

•  - Sample Space: The set of all possible outcomes.

•  - Events: A subset of the sample space.

• - Probability Values: Ranges from 0 to 1.

• Engineers use probability to predict failures and improve reliability.

•Key applications:

•  - Quality control in manufacturing.

•  - Risk assessment in civil engineering.

•  - Reliability analysis of electronic components.

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Fundamentals of Probability in Engineering

- A probability distribution describes how probabilities are distributed over values.

Two types:

•   Discrete distributions (e.g., Binomial, Poisson)

•   Continuous distributions (e.g., Normal, Exponential)

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PROBABILITY
DISTRIBUTION
OVERVIEW

Fundamentals of probability in engineering application

NORMAL DISTRIBUTION

Binomial distribution

Poisson distribution

Exponential distribution

Central Limit Theorem and Its Significance

Reliability assessment of circuits and systems.

ELECTRICAL ENGINEERING

Predicting failure probabilities of materials and structures.

​​STRUCTURAL ENGINEERING

Evaluating component failure risks.

AEROSPACE
ENGINEERING

Quality control, defect detection, and process optimization.

MANUFACTURING

SUMMARY 1.0

Probability theory is a fundamental concept in engineering applications, helping to assess uncertainties and make informed decisions. This module covers key probability distributions and their applications in real-world engineering scenarios.

• Fundamentals of Probability: Probability is the measure of an event's likelihood, calculated as the ratio of favorable outcomes to total possible outcomes.

• Normal Distribution: A continuous distribution defined by mean () and standard deviation (), commonly used in quality control and error analysis.

• Binomial Distribution: A discrete probability model used for success/failure experiments, useful in reliability testing.

SUMMARY 1.1

• Poisson Distribution: Models rare events over time or space, applied in failure rate predictions and traffic analysis.

• Exponential Distribution: Represents time between occurrences in a Poisson process, used in reliability studies.

• Central Limit Theorem: States that the sum of independent variables approaches a normal distribution, essential for statistical inference.

• Engineering Applications: Probability theory is widely used in structural integrity assessments, electrical reliability, aerospace risk analysis, manufacturing quality control, and AI-based decision-making.