7. Probability Distribution Function (PDF)
Probability Distribution Functions (PDFs) provide a mathematical framework for handling uncertainty and randomness in engineering and applied sciences. Key topics include the definitions and properties of PDFs, the relationship between PDFs and cumulative distribution functions (CDFs), common probability distributions, and their applications in various engineering fields. Additionally, PDFs are crucial for solving Partial Differential Equations like the Fokker-Planck equation, linking randomness to time-evolving systems.
Enroll to start learning
You've not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.
Sections
Navigate through the learning materials and practice exercises.
What we have learnt
- A Probability Distribution Function (PDF) defines how the probability is distributed over a range of values for a continuous random variable.
- PDFs are essential in stochastic modeling, signal processing, and probabilistic analysis of engineering systems.
- Key properties of PDFs include non-negativity and normalization, which help calculate probabilities, expected values, and variances.
- PDFs play a significant role in Partial Differential Equations, such as the Fokker-Planck Equation, connecting randomness with physical systems.
Key Concepts
- -- Random Variable
- A function that assigns a numerical value to each outcome in a sample space of a random experiment.
- -- Probability Distribution Function (PDF)
- A function that describes the likelihood of a continuous random variable taking on a specific value.
- -- Cumulative Distribution Function (CDF)
- The function that defines the probability that a random variable X is less than or equal to a certain value.
- -- Mean (Expected Value)
- The average value of a random variable, calculated as the integral of the variable multiplied by its PDF.
- -- Variance
- A measure of the dispersion of a set of values; calculated using the square of the difference from the mean.
Additional Learning Materials
Supplementary resources to enhance your learning experience.