Computing the mean and the variance

Reference no: EM13985433

We have seen that if we superposition a fixed number of Poisson process we obtain a new Poisson process. This need however not be true if we superposition a random number of such processes. More precisely, let us superposition N ∈ Fs(p) independent Poisson processes, each with the same intensity λ, where N is independent of the Poisson processes.

(a) Show that the new process is not a Poisson process, e.g., by computing its generating function, or by computing the mean and the variance (which are equal for the Poisson distribution).

(b) Find (nevertheless) the probability that the first occurrence occurs in process number 1.

Reference no: EM13985433

Questions Cloud

Time of the last occurrence in the time interval : In the previous example, let, instead, T be the time of the last occurrence in the time interval (0, t]. If there is no occurrence during (0, t], we set T = 0. Compute E T.

How far is the object image from the mirror : You have a concave spherical mirror with a 1 0.7-cm radius of curvature. You place an object on the mirror's axis, 18.9 cm in front of the mirror. How far is the object's image from the mirror?

Two parallel wires are carrying currents in same directictio : Q1. In the ?gure, suppose the switch has been closed for a very long time. The resistors have values: R1 = 20.0 ?, R2 = 30.0 ?, R3 = 15.0 ? ...Q2. Two parallel wires are carrying currents in the same direction (to the right, as shown above).

A city wants to know the amount of recycling collected : They know from previous experience that the standard deviation is 1.5. City officials take a random sample of 26 days and calculate a sample mean of 4.1 tons of recycling.

Computing the mean and the variance : Show that the new process is not a Poisson process, e.g., by computing its generating function, or by computing the mean and the variance (which are equal for the Poisson distribution). Find (nevertheless) the probability that the first occurrence..

Compute the generating function of the number : The number of jobs brought to the center by the customers are independent random variables whose common generating function is g(u). Compute the generating function of the number of jobs brought to the computer center during the time interval (s, ..

Compute the expected value of the total amplitude : We finally assume that the initial amplitudes of the pulses are independent of the Poisson process. Compute the expected value of the total amplitude at time t.

Explain why such a small figure is plausible : Studies have concluded that the dead weight loss of monopoly power in the United States is less than 0.5 percent of GNP. From your knowledge of the determinants of the dead-weight loss, explain why such a small figure is plausible.

Compute the expected value of the total waiting time : Compute the expected value of the total waiting time of all passengers who have come to the station in order to catch a train that leaves at time t.

User Account

All Pages