Variance of Discrete Random Variable
Variance measures the spread of a random variable about its mean, calculated as Var(X) = E[(X - μ)²] = E(X²) - [E(X)]², where E(X) = μ is the expected value.
Real World
Netflix measures variance in viewing time per user: a high variance means some users watch 10 minutes while others watch 6 hours, helping them calibrate recommendation algorithms.
Exam Focus
Always use Var(X) = E(X²) − [E(X)]²; build E(X²) by summing x²·P(X=x) before subtracting the mean squared.
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