Reference no: EM132850983

Suppose that the login times to a computer network follows a Poisson process with an average of 4 logins per minute.

a) Find the probability of exactly 6 logins in 2 minutes.

b) What is the mean time between logins (in seconds)?

c) What is the standard deviation of the time between logins (in seconds)?

d) Determine the value of x for which the probability that the first login happens before time x seconds is exactly 0.8.

(Hint: In the Poisson distribution the random variable is the number of events in a time interval, such as number of logins per unit as in our question. But in the sections b, c, and d of the question, mentioned random variable is the length of time between two successive event (or more general, how much time between a given numbers of event). Obviously, this distribution can also use ?? but, here it becomes the rate of occurrence and its unit is 1/time ( but in Poisson distribution ?? is expected number of occurrence, as mentioned before, it is unitless), therefore the distribution function becomes different from Poisson distribution. Decide first which distribution you must use than compute random variable).