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If mean of a poisson distribution of a random variable \(X\) is 2 , then the value of \(P(X > 1.5)\) is
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Verified Answer
The correct answer is:
\(1-\frac{3}{e^2}\)
Since, \(\mathrm{P}(\mathrm{X}=\mathrm{r})=\frac{e^{-\lambda} \lambda^r}{r !}\) (where \(\lambda=\) mean)
\(\begin{aligned}
\therefore \quad & \mathrm{P}(\mathrm{X}=\mathrm{r} > 1.5)=\mathrm{P}(2)+\mathrm{P}(3)+\ldots \infty \\
& =1-\mathrm{P}(\mathrm{X}=\mathrm{r} \leq 1)=1-\mathrm{P}(0)-\mathrm{P}(1) \\
& =1-\left(e^{-2}+\frac{e^{-2} \times 2}{1 !}\right)=1-\frac{3}{e^2}
\end{aligned}\)
\(\begin{aligned}
\therefore \quad & \mathrm{P}(\mathrm{X}=\mathrm{r} > 1.5)=\mathrm{P}(2)+\mathrm{P}(3)+\ldots \infty \\
& =1-\mathrm{P}(\mathrm{X}=\mathrm{r} \leq 1)=1-\mathrm{P}(0)-\mathrm{P}(1) \\
& =1-\left(e^{-2}+\frac{e^{-2} \times 2}{1 !}\right)=1-\frac{3}{e^2}
\end{aligned}\)
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