Domebytes

📘 Day 0 — Probability Basics + PMF & PDF

Start: Nov 16 — Mode A (zero-knowledge). Use this page to learn & post on your blog.

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):

1. A bag has 4 green and 6 yellow balls. Find P(green).
2. Dice: Find P(number > 3).
3. Is height PMF or PDF?

Reply with your answers in comments or here and I'll check.