Students arrive for the much dreaded JEE Advanced according to a Poisson process with rate lambda. For the sanitization process, they must stand in a queue, each student can take a different time or the same time compared with some other student for sanitization. Let us denote the time taken by ii the student as Xi. Xi is independent identically distributed random variables. We assume that Xi takes integer values in range 1,2, ..., n, with probabilities p1, p2, ..., pn . Find the PMF for Nt, the number of students in the sanitization queue at time t.

Students arrive for the much dreaded JEE Advanced according to a Poisson process with rate lambda. For the sanitization process, they must stand in a queue, each student can take a different time or the same time compared with some other student for sanitization. Let us denote the time taken by ii the student as Xi. Xi is independent identically distributed random variables. We assume that Xi takes integer values in range 1,2, ..., n, with probabilities p1, p2, ..., pn . Find the PMF for Nt, the number of students in the sanitization queue at time t.

Name: Students arrive for the much dreaded JEE Advanced according to a Poiss
Uploaded: 2024-03-20T07:06:41.000Z
Channel: Bartleby
Description: Students arrive for the much dreaded JEE Advanced according to a Poisson process with rate lambda. For the sanitization process, they must stand in a queue, each student can take a different time or the same time compared with some other student for

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...

See similar textbooks

Similar questions

Suppose that40%of the applicants for a certain job possess advanced training in computerprogramming. Applicants are interviewed sequntially and are selected at random from the pool. Find theprobability that the 4th applicant with advanced training in programming is found on the 8th interview.To answer this question, first identify the random variable, its distribution and the parameter(s) of the distribution.
Mark and John have decided to meet at the Pub 'Born to be Stochastic' between noon and 1pm without waiting for more than 15 min for each other. Assume Mark and John's arrival times at the Pub are independent random variables that are uniformly distributed in the time interval from noon to 1pm. Compute the probability of Mark and John meeting at the Pub.
3. (Competing patterns among coin flips) Suppose that Xn, n > 1 are i.i.d. random variables with P(X1 = 1) = P(X1 = 0) = }. (These are just i.i.d. fair coin flips.) Let A = (a1, a2, a3) = (0, 1, 1), B = (b1, b2, b3) = (0,0, 1). Let TA = min(n 2 3: {Xn-2, Xn-1, Xn) = A} be the first time we see the sequence A appear among the Xn random variables, and define TB similarly for B. Find the probability that P(TA < TB). (This is the probability that THH shows up before TTH in a sequence of fair coin flips.)
Let E and F be two events of an experiment with sample space S. Suppose P(E) = 0.46, P(F^) = 0.65, and P(E U F) =0.7. Calculate the probabilities below. (a) P(E) = (b) P(F) (c) P(E n F) =
Chains "A" and "B" are made of the same steel. "A" consists of three links and "B" consists of six links, each link having a normal distribution function of the resisting strength with a mean of 60,000 psi and standard deviation of 5,000 psi. Determine which chain is generally weaker (from a probabilistic point of view) by plotting the probability distribution functions of their resisting strengths on the same diagram.
From yrs of teaching experience , an english teacher knows that her student's score will be va random variabel between variance = 25 adn mean = 75 how many students in general ,would have to take exam with a probability of atleast 0.9 , such that the class average would be within 5 of 75 dont use CLT , use markov /Chevyshev
Assume that arrivals of cars at a gas station can be modeled by a Poisson process with rate 2 cars per hour. What is the probability that one has to wait at least 3 hours for the arrival of 3 cars?
In the first hour of customers using the app they served 180 customers. STACO decided to treat this hour as 60 non-overlapping intervals of one minute each. They then assumed they could model the number of customers served each minute by independent and identically distributed Poisson Random Variables. They called the number of customers served in the ith minute X₁, so X₁ + X₂ + ... + X60 180, X₁~ Poisson(X), and X; and X, are independent if i j. - STACO used this to compute an estimated 95% confidence interval and then told Coffee Kart that they could claim to serve an average of three customers per minute. = i Recall that the maximum likelihood estimator of A is A X. Using the same assumptions as STACO and assuming that n is large enough to apply the Central Limit Theorem, calculate an estimated 95% confidence interval for X. ii Do you agree with the assumptions made by STACO. Justify your answer.
6. A transportation department is considering placing stop lights at a busy 4-way-stop intersection. Let X1, X2, X3, X4 represent the number of drivers arriving per minute at the respective stop signs. Assume- these to be four mutually independent Poisson random variables with respective means of 2, 5, 4 and 2. (a) Find the mean and standard deviation of S = Xị. (b) Confirm that S ~ Poisson(13) (c) Compute P(S = 0).
24. Gaussian random variables X, and X,, for which, X, = 2, o = 9, X, =-1, ox, = 4 and Cxx, =-3, are transformed to new random variables Y, and Y, according to जापर डेरें| Y, =-X, + X, Y, =-2X,- 3X, (iii) Cy,Cy, .. Find
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the mean of the given probability distribution. 6) In a certain town, 40% of adults have a college degree. The accompanying table describes the probability distribution for the number of adults (among 4 randomly selected adults) who have a college degree. 6) P(x) 0|0.1296 10.3456 2 0.3456 3 0.1536 4 0.0256 A) µ= 1.73 B ) μ= 2.00 Ομ= 16 D) µ = 1.50