Probability Density | Prey Predator Model | Solved Example

In this video, you’ll explore two foundational topics in applied mathematics — Probability Density Functions (PDFs) and coupled Differential Equation models — through clear, real-world examples.

We’ll start by analyzing the exponential distribution of a satellite’s lifetime, calculating survival probabilities, average life, and interval-based failure chances using the PDF. You’ll learn how to interpret the exponential decay, apply survival functions, and solve common probability questions step-by-step.

Next, we dive into a predator-prey system modeled by nonlinear differential equations. You’ll see how to simulate population dynamics using a numerical method, identify the equilibrium point, and discuss its stability using Jacobian analysis — all explained intuitively.

By the end of the tutorial, you’ll not only gain strong conceptual understanding but also practical skills in simulation, stability analysis, and interpreting mathematical models across statistics and dynamic systems.

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Chapters in the video:
0:00 Introduction
0:37 Problem Statement (Probability Density)
01:04 Solving The Problem
05:20 Concept Recap
06:07 Problem Statement (Prey Predator Model)
07:15 Parameter Meanings
07:56 Simulation
09:34 Stability in Equilibrium
12:34 Conclusion

Background Music Credits (in order of use)
Outro Music Credit:
Spirit by Sappheiros:
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