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Random Variables and Probability Distributions

Telangana Board · Class 12 · Mathematics

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

133 questions20 flashcards5 concepts

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Key Topics to Revise

1

Random Variables - Definition and Types

  • A random variable is a function X: S → R that assigns real numbers to outcomes of a random experiment
  • Random variables convert outcomes into measurable quantities for mathematical analysis
  • Discrete random variables have countable outcomes (finite or countably infinite)
2

Probability Distribution of Discrete Random Variables

  • Probability distribution lists all possible values and their probabilities
  • Two fundamental conditions: P(xi) ≥ 0 and Σ P(xi) = 1
  • Can be represented in tabular form for easy visualization
3

Mean, Variance and Standard Deviation

  • Mean (μ) represents the expected value or average outcome
  • Variance (σ²) measures spread or dispersion of the distribution
  • Standard deviation (σ) is the square root of variance
4

Binomial Distribution

  • Models number of successes in n independent Bernoulli trials
  • Has two parameters: n (trials) and p (success probability)
  • Each trial has only two outcomes: success (p) or failure (q = 1-p)

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Full Notes

Key Concepts

A random variable X isDiscrete random variables take finiteA probability distribution shows all possibleMean μ = Σ xi P(xi)Variance σ² = Σ (xi

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Sources & Official References

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

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