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Probability Distributions — Syllabus

Tamil Nadu Board · Class 12 · Mathematics

What Probability Distributions covers in Tamil Nadu Board Class 12 Mathematics: 4 topics, for the 2026-27 session.

45 questions20 flashcards5 formulas & key relations5 concepts

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4 Topics · Tamil Nadu Board Class 12 Mathematics · 2026-27

Topics in Probability Distributions

1

Random Variables

  • A random variable X is a function from the sample space S to the real numbers R, i.e., X: S → R
  • Random variables are denoted by capital letters (X, Y, Z) and their values by small letters (x, y, z)
  • The range set R_x = {X(ω) / ω ∈ S} is the set of all possible values of X
2

Discrete Random Variables and Probability Mass Function (PMF)

  • A discrete random variable X has a countable (finite or countably infinite) range set
  • The Probability Mass Function (PMF) f(x) gives the probability that X takes value x: f(xₖ) = P(X = xₖ)
  • Two conditions for a valid PMF: (i) f(xₖ) ≥ 0 for all k, and (ii) Σf(xₖ) = 1
3

Cumulative Distribution Function (CDF)

  • CDF F(x) = P(X ≤ x) gives the probability that X takes a value less than or equal to x
  • CDF is defined for all real numbers x ∈ R, even though PMF is only defined at discrete points
  • CDF is a step function for discrete random variables — it jumps at each value xₖ
4

Continuous Random Variables and Probability Density Function (PDF)

  • A continuous random variable X takes values in an interval — uncountably many values
  • For continuous X: P(X = a) = 0 for every single value a — probability at a point is ZERO
  • The Probability Density Function (PDF) f(x) satisfies: (i) f(x) ≥ 0 and (ii) ∫_{-∞}^{∞} f(x)dx = 1

Key Concepts

A random variable X isA random variable that takes onFor a discrete random variable XFor any random variableA random variable that can take

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Frequently Asked Questions

What are the important topics in Probability Distributions for Tamil Nadu Board Class 12 Mathematics?
Key topics in Probability Distributions include Random Variables, Discrete Random Variables and Probability Mass Function (PMF), Cumulative Distribution Function (CDF), Continuous Random Variables and Probability Density Function (PDF). Study these first, then practise questions on each for the Tamil Nadu Board Class 12 board exam.
How should I revise Probability Distributions for the Tamil Nadu Board Class 12 board exam?
Learn the core ideas first, then work through the 45 practice questions on Probability Distributions. Revise definitions regularly and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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All Tamil Nadu Board Class 12 Mathematics Syllabus

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