AP EAMCET · Maths · Probability
If \(X\) is a poisson variate such that \(\alpha=P(X=1)=P(X=2)\), then \(P(X=4)\) is equal to
- A \(2 \alpha\)
- B \(\frac{\alpha}{3}\)
- C \(\alpha e^{-2}\)
- D \(\alpha e^2\)
Answer & Solution
Correct Answer
(B) \(\frac{\alpha}{3}\)
Step-by-step Solution
Detailed explanation
Given \(X\) is a poisson variate such that \(\begin{aligned} & \alpha=P(X=1)=P(X=2) \\ & \frac{e^{-\lambda} \lambda}{1 !}=\frac{e^{-\lambda} \lambda^2}{2 !} \Rightarrow \lambda=2 \\ & \alpha=P(X=1) \\ & \quad=e^{-2} \times 2=\frac{2}{e^2}\end{aligned}\)…
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