If X has Poisson distribution with m = 1, then find P(X ≤ 1) give… - Vidyadip

Question

If $X$ has Poisson distribution with $m = 1$, then find $P(X ≤ 1)$ given $e^{-1} = 0.3678.$

✓

Answer

$
\because m=1
$
$\because X$ follows Poisson Distribution
$
\begin{aligned}
& \therefore \quad p(x)=\frac{e^{-m} \cdot m^x}{x !} \\
& P ( X \leq 1)=p(0)+p(1) \\
& =\frac{e^{-1} \times 1^0}{0 !}+\frac{e^{-1} \times 1^1}{1 !}
\end{aligned}
$
$
\begin{aligned}
& = e ^{- m } \times 1+ e ^{- m } \times 1 \\
& = e ^{-1}+ e ^{-1} \\
& =2 \times e ^{-1} \\
& =2 \times 0.3678 \\
& =0.7356
\end{aligned}
$

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