Random Variables and Probability Distributions

Kerala Board · Class 12 · Mathematics

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

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Key Topics to Revise

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)

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

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

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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