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TS EAMCET · Maths · Probability

For a poisson variate \(X\), if \(P(X=2)=3 P(X=3)\), then the mean of \(X\) is :

  1. A 1
  2. B \(\frac{1}{2}\)
  3. C \(\frac{1}{2}\)
  4. D \(\frac{1}{4}\)
Verified Solution

Answer & Solution

Correct Answer

(A) 1

Step-by-step Solution

Detailed explanation

We know that, \(P(X=k)=\frac{\lambda^k e^\lambda}{k !}\) Since, \(P(X=2)=3 P(X=3)\) \(\Rightarrow \quad \frac{\lambda^2 e^\lambda}{2 !}=3 \cdot \frac{\lambda^3 e^\lambda}{3 !} \Rightarrow \lambda=1\) \(\therefore\) Mean of poisson distribution \(=\lambda\) \(=1\)
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