Help me with the following question...all parts should be answered in details for my understanding

X is a positive stochastic continuous variable with probability distribution func- tion (PDF) F(x) = P(X I). c) Calculate the Laplace Transform f*(s) = E[e-*] = [* e->If(x)dx. d) Calculate the expected values m = E[X], E[X*], k = 0, 1,2, ..., the vari- ance of, the standard deviation ox and the coefficient of variation c = o/m, with and without the transform F* (s).2.3 Exercise 3.4 Consider a communication link with a constant rate of 4.8kbit/sec. Over the link we transmit two types of messages, both of exponentially distributed size. Messages arrive in a Poisson fashion with A = 10 messages/second. With prob- ability 0.5 (independent from previous arrivals) the arriving message is of type 1 and has a mean length of 300 bits. Otherwise a message of type 2 arrives with a mean length of 150 bits. The buffer at the link can at most hold one message of type 1 or two messages of type 2. A message being transmitted still takes a place in the buffer. a) Determine the mean and the coefficient of variation of the service time of a randomly chosen arriving message. b) Determine the average times in the system for accepted messages of type 1 and 2. c) Determine the message loss probabilities for messages of type 1 and 2.2.4 Exercise 3.5 Consider a Markovian system with discouraged job arrivals. Jobs arrive to a server in a Poisson fashion, with an intensity of one job per 7 seconds. The jobs observe the queue. They do NOT join the queue with probability l if they observe k jobs in the queue. Ik = k/4 if k roz*px. Calculate P(2) for the system. Note, that P(2) must be finite for (2)