IAI Actuarial Core Principles · Actuarial Statistics · Basic univariate distributions and generating samples
A Poisson random variable X has P(X=1) = P(X=2). What is the value of P(X=0)?
Equating λe^-λ with λ²e^-λ/2 gives λ = 2, so P(X=0) = e^-2 = 0.1353. The value 0.2707 is the probability of one event, not zero.
- A0.0498
- B0.1353Correct
- C0.2707
- D0.3679
- 0.0183
Explanation
λe^-λ = λ²e^-λ/2 gives λ = 2. Then P(X=0) = e^-2 = 0.1353. The value 0.2707 is P(X=1), not P(X=0).
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