Let X1, X2,. . . , Xn are independent and Xi follows Poisson(Ai) distribution, i = 1,2,... , nUse the probability generating function to show that 1X follows Poisson(i-1 Ai)distribution

As per the questionX ~ Poisson (λ)Moment Generating function is given by

Answered: Let X1, X2,. . . , Xn are independent…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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A delivery truck travels from point A to point B and back using the same route each day. There are four traffic lights on the route. Let X1 denote the number of red lights the truck encounters going from A to B and X2 denote the number encountered on the return trip. Data collected over a long period suggest that the joint probability distribution for (X1, X2) is given by Please show complete solution.
Q/C/ If the disjoint events A and B such that P(B)=1/3 , then the value of P(Bn A) is------.
There are two boxes. In each box there are 4 cards with a different number printed on it. The four cards have been numbered as 1,2,3,4 in each box. Two cards are drawn random from each box. The random variable X represents the difference between the number on the card from box 1 minus the number on the card from box 2.a) Find the mean of this probability distribution. (i.e. Find E[X] )b) Find the variance and standard deviation of this probability distribution.(i.e. Find V[X] and SD[X])The random variables M and W are defined as follows:M = X+5 and W = (1/2)X+5c) Find E[M] and E[W].d) Find V[M] and V[W].e) Mary and William play a game using the cards in the above boxes. Randomly two cards are drawn, and Mary records his score using the random variable M and William uses the random variable W. They repeat this for a large number of times and compare their scores. Comment on any likely differences or similarities of their scores.
HH=2, JJ=1, LL=3, NN=fifth (5th)
An average of 1 package is sent to a server in 1 second. The server, on the other hand, prepares a document using the 5 packages received. The time between packets is modeled as an exponential random variable. Let X be a random variable expressing the time it takes the server to prepare a document. The time taken to prepare a document; a) Find the probability that it is more than 10 seconds.(with detail) b) Find the probability that it is between 5 seconds and 10 seconds. (with detail)
The time between busses on Stevens Creek Blvd is 12 minutes. Therefore the wait time of a passenger who arrives randomly at a bus stop is uniformly distributed between 0 and 12 minutes. Find the probability that a person randomly arriving at the bus stop to wait for the bus has a wait time of at most 5 minutes.
The flow of goods through a certain machine in a factory can be modeled as a Poisson Random Process. Suppose that a machine has 20 goods per minute as an outflow rate, determine the probability that the 7th good will exit within 30 seconds. (Express your answer in 4 decimal places)
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The cycle time for trucks hauling concrete to a highway construction site is uniformly distributed over the interval 50 to 70 minutes. a) Find the probability distribution function f(x). Define the random variable x is a continuous random variable or discrete random variable. b) What is the probability that the cycle time exceeds 65 minutes?
The time between arrivals of customers at an automatic teller machine (ATM) is an exponential random variable with a mean of five minutes. a) What is the probability that the time until the third customer arrives in more than 10 minutes? b) what is the value for σ2 for the third customer? c) what is the value for σσ for the third customer ?

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Let X1, X2,. . . , Xn are independent and Xi follows Poisson(Ai) distribution, i = 1,2,... , n Use the probability generating function to show that 1X follows Poisson(i-1 Ai) distribution