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