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Probability Distributions

Tamil Nadu Board · Class 12 · Mathematics

Quick revision notes for Probability Distributions — Tamil Nadu Board Class 12 Mathematics. Key concepts, formulas, and definitions for last-minute revision.

45 questions20 flashcards5 concepts

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Key Topics to Revise

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

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Full Notes

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

Frequently Asked Questions

What are the important topics in Probability Distributions for Tamil Nadu Board Class 12 Mathematics?
Key topics in Probability Distributions include Probability Distributions - Complete Chapter Overview, Problem-Solving Strategy for Probability Distribution Problems, Shows how a random variable maps sample space outcomes to real numbers. These are the concepts Tamil Nadu Board Class 12 examiners draw on most — study them first, then practise related questions.
How to score full marks in Probability Distributions — Tamil Nadu Board Class 12 Mathematics?
Understand the core concepts first, then work through the 45 practice questions available for this chapter. Revise formulas and 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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