Skip to content

FRM Part I · FRM Exam Part I · Common Univariate Random Variables

Operational loss events at a bank arrive following a Poisson process with an average of 3 events per month. What is the probability that exactly 2 events occur in a given month?

The probability is 0.2240. Using the Poisson formula with lambda = 3, P(X=2) = e^-3 × 3^2 / 2 = 0.0498 × 4.5, which is about 0.2240. The cumulative probability of at most two events would be larger, at 0.4232.

  1. A0.2240Correct
  2. B0.1494
  3. C0.0498
  4. D0.4232

Explanation

Poisson with lambda=3: P(2)=e^-3 × 3^2/2! = 0.049787 × 4.5 = 0.2240. The 0.0498 option is P(0), and 0.1494 is P(1)... in fact P(1)=0.1494. The 0.4232 option is P(at most 2) = 0.0498+0.1494+0.2240 = 0.4232.

Did you get it right without looking?

One question tells you little. A timed set on Common Univariate Random Variables shows your real accuracy, how long you take and where you lose marks.

Practise Common Univariate Random VariablesFree diagnostic mock

More Common Univariate Random Variables questions