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TS EAMCET · Maths · Probability

If \(\mathrm{X}\) is a Poisson variate such that \(\frac{5}{3} k=P(\mathrm{X}=2)\) \(=P(\mathrm{X}=3)\), then \(P(\mathrm{X}=5)=\)

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

Answer & Solution

Correct Answer

(D) \(\frac{3}{4} k\)

Step-by-step Solution

Detailed explanation

\begin{aligned} & \text {} \frac{5}{3} \mathrm{k}=\frac{\mathrm{e}^{-\lambda} \lambda^2}{2 !}=\frac{\mathrm{e}^{-\lambda} \lambda^3}{3 !} \\ & \frac{\mathrm{e}^{-\lambda} \lambda^2}{2 !}=\frac{\mathrm{e}^{-\lambda \lambda 3}}{3 !} \Rightarrow \lambda=3 \\ & \therefore…