AP EAMCET · Maths · Probability
Suppose that a random variable \(X\) follows Poisson distribution. If \(P(X=1)=P(X=2)\) then \(P(X=5)\) is equal to
- A \(\frac{2}{3} e^{-2}\)
- B \(\frac{3}{4} e^{-2}\)
- C \(\frac{4}{15} e^{-2}\)
- D \(\frac{7}{8} e^{-2}\)
Answer & Solution
Correct Answer
(C) \(\frac{4}{15} e^{-2}\)
Step-by-step Solution
Detailed explanation
Let \(\lambda\) be the mean of the poisson variate \(x\). Then, \(P(X=r)=\frac{\lambda^r e^{-\lambda}}{r !}, r=0,1,2, \ldots\) Now, \(P(X=1)=P(X=2) \Rightarrow \frac{\lambda e^{-\lambda}}{1 !}=\frac{\lambda^2 e^{-\lambda}}{2 !}\) \(\Rightarrow \quad \lambda=2\) Hence,…
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