Probability Distributions · Class 12 Applied Mathematics · Chapter 4
🎲 Probability Distributions
CBSE Class 12 Humanities & Commerce · Applied Mathematics · Chapter 1
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| 80% | Construct probability distribution from a small experiment — List sample space · count outcomes for each X-value · build the table · CHECK Σ p_i = 1. | 3 MARKS |
| 85% | E(X) and Var(X) from a distribution table — E(X) = Σ x_i·p_i · E(X²) = Σ x_i²·p_i · Var = E(X²) − [E(X)]². Tabulate to avoid slips. | 3 MARKS |
| 95% | Binomial P(X = k) and/or mean & variance — Identify n, p · PMF C(n,k) p^k (1−p)^(n−k) · mean = np, variance = np(1−p). Don't forget the nCr factor. | 5 MARKS |
| 70% | Poisson rare-event count — Identify λ · use given e^(−λ) hint · P(X = k) = e^(−λ)·λ^k/k! · P(X ≥ 1) = 1 − P(X = 0). | 4 MARKS |
| 75% | Normal distribution z-table look-up — Standardise z = (X − μ)/σ · use Φ(z) directly (left tail) · take 1 − Φ(z) for right tail · between: Φ(b) − Φ(a). | 4 MARKS |
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