Teaching CSIR NET Mock Test Series Mathematical Science Statistics & Exploratory Data Analysis Probability Inequalities
Consider a scenario where customers arrive at a bank following a Poisson distribution at the rate of 6 per hour. The time taken for each service is exponentially distributed and the single available bank clerk takes an average of 8 minutes to service each customer. Assuming that customers leave immediately after they are serviced, let γ denote the probability of finding 2 or more customers waiting in line and let δ denote the mean number of customers in the queue.
Which of the following statements are correct?
1
γ is a non-zero value and depends on the rate of customer arrival and service time.
2
The arrival of customers and their service times are independent events.
3
The bank needs to increase the service rate and/or decrease the customer arrival rate to reduce γ and δ.
4
The steady-state probability that there are no customers waiting in line at any given moment is less than 0.5.