1. ## probability

1, In a particular departmental store customers arrive at a check up counter
according to poisson distribution at an average of 5 per hour
During a particular 1 hour period,
a,what is the probability that at least 3 customers will arrive
b,What is the probability that in a given 2 hours period exactly 2 customers will arrive
c,In a 30 minute period determine the probability that at most 2 customers will arrive

2. so we know that are $\lambda = 5$, so for:

a) $P(X \geq 3) = P(X=3) \cup P(X=4) \cup P(X=5)$

$P(X \geq 3) = \frac{5^3}{3!}e^{-5}+\frac{5^4}{4!}e^{-5} + \frac{5^5}{5!}e^{-5}$

b) $\lambda = 2 \times 5 = 10$

$P(X = 2 ) = \frac{10^2}{2!}e^{-10}$

c) $\lambda = \frac{1}{2} \times 5 = \frac{5}{2}$

$P(X \leq 2) = P(X=0) \cup P(X=1) \cup P(X=2)$

$P(X \leq 2) = \frac{2.5^0}{0!}e^{-2.5}+\frac{2.5^1}{1!}e^{-2.5} + \frac{2.5^5}{2!}e^{-2.5}$