Module 3 · Distributions · Topic 2
Discrete Random Variables. A discrete random variable takes countable values (e.g., 0, 1, 2, ...). Its probabilities are described by a probability mass function (PMF).
Continuous Random Variables. A continuous random variable takes any value in an interval. Its probabilities are described by a probability density function (PDF). The probability at any exact point is 0; probabilities are found over intervals.
Key Difference. For discrete variables, we sum probabilities: P(X = k). For continuous variables, we integrate the PDF over an interval: P(a ≤ X ≤ b) = area under the curve between a and b.
P(X = k) = C(n,k)p^k(1-p)^(n-k) — Exact probability of k successes in n independent Bernoulli trials.z = (x - mu) / sigma — Standardizes a value by measuring standard deviations from the mean.Discrete: number of customers per hour, number of heads in 10 flips. Continuous: height, weight, time to complete a task.
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