🟢 Stats: The Key Distributions

Normal Distribution - Bell-shaped, symmetric, defined by mean (μ) and std dev (σ) - 68-95-99.7 rule: 68% within ±1σ, 95% within ±2σ, 99.7% within ±3σ - Central Limit Theorem makes this universal — sample means are always ~normal

Binomial Distribution - Count of successes in n independent trials, each with probability p - Mean = np, Variance = np(1-p) - "Out of 100 users, how many click if click rate is 5%?" → Binomial(100, 0.05), mean = 5

Poisson Distribution - Count of events in a fixed interval - Mean = λ, Variance = λ (they're equal!) - "How many support calls per hour?" — if mean = 4, variance = 4 too - Tip: if you see a count distribution where mean ≈ variance, it's likely Poisson

Exponential Distribution - Time BETWEEN events (complement of Poisson) - Mean = 1/λ - Memoryless: how long you've waited doesn't affect how much longer you'll wait - "How long until the next customer arrives?"