Geometric Distribution
The geometric distribution models the number of independent Bernoulli trials X required until the first success, where each trial has probability p of success. The probability mass function is P(X = k) = (1-p)^(k-1) × p, where k = 1, 2, 3, ... The mean is E(X) = 1/p and the variance is Var(X) = (1-p)/p².
Real World
A recruitment manager at Deloitte finds that roughly 1 in 8 graduate applicants passes the final interview, so she models the number of interviews needed to fill one position using a geometric distribution with p = 0.125.
Exam Focus
State the memoryless property if asked to justify the model — and confirm trials are independent with constant probability p each time.
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