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Probability Distributions

Maharashtra Board · Class 12 · Mathematics & Statistics - Science

Quick revision notes for Probability Distributions — Maharashtra Board Class 12 Mathematics & Statistics - Science. Key concepts, formulas, and definitions for last-minute revision.

45 questions20 flashcards5 concepts

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Key Topics to Revise

1

Random Variables - Foundation

  • A random variable assigns a unique real number to every possible outcome of a random experiment
  • Random variables are denoted by capital letters (X, Y, Z) and their values by small letters (x, y, z)
  • The set of all possible values is called the range or support of the random variable
2

Discrete Random Variables and Probability Mass Function

  • Discrete random variables have finite or countably infinite possible values
  • Probability Mass Function (PMF) gives P(X = x) for each possible value x
  • Sum of all probabilities equals 1: Σ P(X = xᵢ) = 1
3

Expected Value and Variance - Solved Examples

  • Expected value E(X) is the weighted average of all possible values
  • Variance Var(X) measures spread or dispersion around the mean
  • Standard deviation σ = √Var(X) gives measure of spread in original units
4

Continuous Random Variables and PDF

  • Continuous random variables have uncountably infinite values forming intervals
  • Probability Density Function (PDF) f(x) gives relative likelihood, not actual probability
  • P(X = x) = 0 for any specific value x in continuous case

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Full Notes

Key Concepts

A random variable is a realA discrete random variable can takeA continuous random variable can takeFor a discrete random variable XFor a continuous random variable X

Frequently Asked Questions

What are the important topics in Probability Distributions for Maharashtra Board Class 12 Mathematics & Statistics - Science?
Probability Distributions covers several key topics that are frequently asked in Maharashtra Board Class 12 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Probability Distributions — Maharashtra Board Class 12 Mathematics & Statistics - Science?
Start by understanding all key concepts. Practise previous year questions from this chapter. Revise formulas and definitions regularly. Use flashcards for quick revision 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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