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TS EAMCET · Maths · Probability

If a poisson variate \(X\) satisfies \(P(X=2)\) \(=P(X=3)\), then \(P(X=5)=\)

  1. A \(\frac{81}{40 e^5}\)
  2. B \(\frac{81}{40 e^3}\)
  3. C \(\frac{243}{40 e^3}\)
  4. D \(\frac{243}{40 e^5}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{81}{40 e^3}\)

Step-by-step Solution

Detailed explanation

According to given information, \(\frac{\lambda^2 e^{-\lambda}}{2 !}=\frac{\lambda^3 e^{-\lambda}}{3 !} \Rightarrow \lambda=3\) So, \(P(X=5)=\frac{3^5 e^{-3}}{5 !}=\frac{81 e^{-3}}{40}=\frac{81}{40 e^3}\) Hence, option (b) is correct.