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 \(P(\mathrm{X}=5)=\)
- A \(k\)
- B \(\frac{1}{4} k\)
- C \(\frac{1}{2} k\)
- D \(\frac{3}{4} k\)
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…
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