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AP EAMCET · Maths · Probability

If ' 3 ' is the variance of Poisson distribution, then \(\mathrm{P}(1 < \mathrm{x} < 4)=\)

  1. A \(\frac{123}{8} e^{-3}\)
  2. B \(3 e^{-\sqrt{3}}\)
  3. C \(9 \mathrm{e}^{-3}\)
  4. D \(\left(\frac{3+\sqrt{3}}{2}\right) e^{-3}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(9 \mathrm{e}^{-3}\)

Step-by-step Solution

Detailed explanation

\(\mathrm{P}(1 < x < 4)=\mathrm{P}(x=2)+\mathrm{P}(x=3)\) \(\begin{aligned} & \mathrm{P}(x=n)=\frac{\lambda^n \cdot e^{-\lambda}}{n !} \\ & \mathrm{P}(x=2)+\mathrm{P}(x=3)=\frac{(3)^2 \cdot e^{-3}}{2 !}+\frac{(3)^3 \cdot e^{-3}}{3 !}\end{aligned}\)…