I checked this forum for any potential help with stochastic processes. I hope there is anybody who could help me with a couple of homework questions/tasks. I would very much appreciate any help and would also be willing to compensate.

I need to provide solutions for the following questions:

1. Variable x has four values: 0,31; 0,49; 0,01 and 0,45. Can x be uniformly

distributed? Elaborate.

2. It takes one minute to buy a ticket. On average, two buyers enter the que

in three minutes. Find the average lenght of the que and the probability

that there is one person in the que. The time it takes to serve a person is

distributes exponentially and a single server mode is studied.

3. The probability of equipment stoping abruptly, during one minute, is 0,2.

Service person checks equipment once in every minute. There is a 0,6

probability that equipment, that has stopped, is going to be fixed within

one minute. Find the probability that equipment is still working after two

minutes, if it was working at the outset.

I have the related book (Basic textbook : H.A.Taha, Operations Research: An Introduction, Prentice Hall) as pdf-file, if required.

Thanks in advance.

Tom