First slide

Random variable and probability distribution

Question

A random variable X has Poisson distribution with mean 2. Then P(X > 1.5) equals

Moderate

A

$\frac{2}{e^{2}}$
B

0
C

$1 - \frac{3}{e^{2}}$
D

$\frac{3}{e^{2}}$

Solution

$P (x = k) = e^{- λ} \frac{λ^{k}}{k!}$
$P (x \geq 2) = 1 - P (x = 0) - P (x = 1) = 1 - e^{- λ} - e^{- λ} (\frac{λ}{1!}) = 1 - \frac{3}{e^{2}}$

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