TS EAMCET · Maths · Probability
If a poisson variate \(X\) satisfies \(P(X=2)\) \(=P(X=3)\), then \(P(X=5)=\)
- A \(\frac{81}{40 e^5}\)
- B \(\frac{81}{40 e^3}\)
- C \(\frac{243}{40 e^3}\)
- D \(\frac{243}{40 e^5}\)
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.
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