📘 Day 0 — Probability Basics + PMF & PDF
What you'll learn today
Probability = the chance of an event happening. Values always lie between 0 and 1.
Random Variable (RV) — a number we give to an outcome.
Example: coin → Heads = 1, Tails = 0; dice → result 1..6.
PMF — Probability Mass Function (very simple)
Used for discrete variables (dice, coin, counts). PMF lists P(X = x) for each possible x.
Example (fair die): P(X=1)=1/6, P(X=2)=1/6, …, P(X=6)=1/6. Sum of all PMF values = 1.
PDF — Probability Density Function (very simple)
Used for continuous variables (time, height). PDF is not a probability at a point — instead probability is area under curve.
Example: f(x)=1 for 0<x<1 → P(0.2<X<0.7)=area=0.5. Total area under PDF = 1.
Quick summary
- PMF → discrete, probabilities add up
- PDF → continuous, area under curve = 1
- Random variable = number representing outcome
📝 Your Notes (saved locally)
🧠 Quick Quiz — (Type short answers)
Q1. Probability always lies between ___ and ___ ?
Q2. PMF is used for (discrete/continuous)?
Q3. Total area under a PDF equals ___ ?
Q4. For continuous RV, probability at an exact point is ___ ? (write number or word)
Practice (do now):
- A bag has 4 green and 6 yellow balls. Find P(green).
- Dice: Find P(number > 3).
- Is height PMF or PDF?
Reply with your answers in comments or here and I'll check.