The deals cracked by an agent per day is a random Poisson variable with mean 2. Given that each day is independent of other day, find the probability of getting 2 deals cracked on first day and 1 deal to be cracked the next day.

Suppose A and B are two events with probabilities:  P(A^c)=.30, P(B/A)=.40 What is (AnB)?

A large ski mountain has a fleet of 4 snowmobiles it uses during the winter season. It believes that the time between consecutive repair operations for a single snowmobile is an exponential random variable with a mean of .75 weeks. There are two dedicated technicians that are capable of repairing the snowmobiles. A broken down snowmobile will be repaired by one of these technicians (when one becomes available) and the repair time of a snowmobile can be modeled as an exponential random variable with a mean of .4 weeks. (a) Describe a queueing system model of the repair operations of the snowmobiles by answering the following questions: What are the customers in the queueing system? What are the servers and what service is being provided? b) Provide the rate transition diagram of the birth and death process that captures the queueing system. Be sure to provide λn and µn for each relevant value of n and your logic behind any calculations used to obtain them (c) Provide the…

Officer Thompson of the Bay Ridge Police Department works the graveyard shift. He averages 4.5calls per shift from this dispatcher. Assume the number of calls follows a Poisson distribution. Find theprobability that Officer Thompson get fewer than 2 calls in a shift.