Customer arrivals at a bank are random and independent. The probability of an arrival in any
one-minute period is same as that in any other one-minute period. Assuming mean arrival rate
of five customers per minute, find the probability of
• Exactly three arrivals in one-minute period
• No arrivals in half-minute period
• Three minutes for next customer to arrive
Answers
Answer:
The arrival of the clients to the bank can be modeled as the Poisson process. The Poisson distribution describes the probability of occurrence of an event in a specified interval of time, given that the average number of occurrence of that event is known and constant.
If XX represents the random occurrence of the event following the Poisson process, then the probability distribution of XX is given as:
P(X)=λxe−λx!P(X)=λxe−λx!, where λλ is the average rate of occurence.
Answer:
Step-by-step explanation:
Answer:
a)0.2240
b)0.5768
Step-by-step explanation:
Given:
µ=3
Poison probability is given by :
a) Evaluating at k=3
b)Evaluating at k=0,1,2:
Use complement rule:
P(x≥3)= 1 - f(0) - f(1) - f(2)= 1- 0.0498 - 0.1494 - 0.2240 =0.5768