AP EAMCET · Maths · Probability
If \(X\) follows Poisson distribution with variance 2, then \(P(X \geq 3)=\)
- A \(\frac{5}{e^2}\)
- B \(5+\frac{2}{e^2}\)
- C \(\frac{e^2-5}{e^2}\)
- D \(\frac{5-e^2}{4}\)
Answer & Solution
Correct Answer
(C) \(\frac{e^2-5}{e^2}\)
Step-by-step Solution
Detailed explanation
\(\lambda = 2\) \(P(X \geq 3) = 1 - [P(X=0) + P(X=1) + P(X=2)]\) \(P(X \geq 3) = 1 - \left(\frac{e^{-2}2^0}{0!} + \frac{e^{-2}2^1}{1!} + \frac{e^{-2}2^2}{2!}\right)\) \(P(X \geq 3) = 1 - (e^{-2} + 2e^{-2} + 2e^{-2})\) \(P(X \geq 3) = 1 - 5e^{-2}\)…
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