First slide

Random variable and probability distribution

Question

Suppose on an average 1 house in 1000 in a certain district has a fire during a year. If there are 2000 houses in that district, the probability that exactly 5 houses will have a firing during a year

Moderate

A

$\frac{1}{15 e^{2}}$
B

$\frac{14}{15 e^{2}}$
C

$\frac{4}{15 e^{2}}$
D

$e^{- 2}$

Solution

$p = \frac{1}{1000}$
$\Rightarrow λ = n p = 2000 \frac{1}{1000} = 2$

$P (X = 5) = \frac{e^{- λ} λ^{5}}{5!} = \frac{e^{- 2} 2^{5}}{5!} = \frac{4}{15 e^{2}}$

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