Busses arrive at a certain stop such that in a time interval of length the number of arrivals is a random variable with probability mass function $$f ( i ) = \left\{ \begin{array} { l l }
e ^ { - t } \frac { \left( t ^ { i } \right) } { i ! } & i = 0,1,2 , \ldots \
0 & \text { elsewhere }
\end{array} \right.$$
(a) Prove that is indeed a probability mass function.
(b) Find the probability of at least 3 arrivals in one time period of length .

Question

Busses arrive at a certain stop such that in a time interval of length the number of arrivals is a random variable with probability mass function $$f ( i ) = \left\{ \begin{array} { l l } 
e ^ { - t } \frac { \left( t ^ { i } \right) } { i ! } & i = 0,1,2 , \ldots \
0 & \text { elsewhere }
\end{array} \right.$$ 
(a) Prove that is indeed a probability mass function.
(b) Find the probability of at least 3 arrivals in one time period of length .

Quizplus · Accepted Answer

The Answer of Busses arrive at a certain stop such that in a time interval of length the number of arrivals is a random variable with probability mass function $$f ( i ) = \left\{ \begin{array} { l l } 
e ^ { - t } \frac { \left( t ^ { i } \right) } { i ! } & i = 0,1,2 , \ldots \
0 & \text { elsewhere }
\end{array} \right.$$ 
(a) Prove that is indeed a probability mass function.
(b) Find the probability of at least 3 arrivals in one time period of length .

Busses Arrive at a Certain Stop Such That in a Time