ExamBro
ExamBro
AP EAMCET · Maths · Probability

If \(X\) follows Poisson distribution with variance 2, then \(P(X \geq 3)=\)

  1. A \(\frac{5}{e^2}\)
  2. B \(5+\frac{2}{e^2}\)
  3. C \(\frac{e^2-5}{e^2}\)
  4. D \(\frac{5-e^2}{4}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{e^2-5}{e^2}\)

Step-by-step Solution

Detailed explanation

\(\lambda = 2\) \(P(X \geq 3) = 1 - [P(X=0) + P(X=1) + P(X=2)]\) \(P(X \geq 3) = 1 - \left(\frac{e^{-2}2^0}{0!} + \frac{e^{-2}2^1}{1!} + \frac{e^{-2}2^2}{2!}\right)\) \(P(X \geq 3) = 1 - (e^{-2} + 2e^{-2} + 2e^{-2})\) \(P(X \geq 3) = 1 - 5e^{-2}\)…