# Question: Consider a Poisson counting process with arrival rate Suppose

Consider a Poisson counting process with arrival rate, λ. Suppose it is observed that there have been exactly arrivals in [0, t] and let S1, S2… Sn be the times of those arrivals. Next, define X1, X2… Xn to be a sequence of IID random variables uniformly distributed over [0, t] and let Y1, Y2… Yn be the order statistics associated with the Xi. Show that the joint PDF of the order statistics, fY (y), is identical to the joint PDF of the Poisson arrival times, fs (s). Hence, the order statistics are statistically identical to the arrival times.

**View Solution:**## Answer to relevant Questions

Model lightning strikes to a power line during a thunderstorm as a Poisson impulse process. Suppose the number of lightning strikes in time interval t has a mean rate of arrival given by s, which is one strike per 3 minutes. ...A random process X (t) is said to be mean square continuous at some point in time t, if (a) Prove that X (t) is mean square continuous at time if its correlation function RX, X (t1, t2), is continuous at the point t1 = t, ...Let a discrete random process X [n] be generated by repeated tosses of a fair die. Let the values of the random process be equal to the results of each toss. (a) Find the mean function, µX [n]. (b) Find the ...A biologist would like to estimate the size of a certain population of fish. A sequential approach is proposed whereby a member of the population is sampled at random, tagged and then returned. This process is repeated until ...A student takes this course at period 1 on Monday, Wednesday, and Friday. Period 1 starts at 7: 25 A. M. Consequently, the student sometimes misses class. The student’s attendance behavior is such that she attends class ...Post your question