Problem 5Suppose that we have designed a randomized algorithm fora problem having "Yes" or "No" answer. The algorithm is such that if the answeris "Yes," it is always correct. If the answer is "No," it is correct withprobability at least 0.02. How many times do we need to run this algorithm inorder to be sure that the probability of getting an erroneous answer is at most0.02?

The problem under study follows a Bernoulli distribution as it has only two possible outcomes "Yes"…

Answered: Problem 5 Suppose that we have designed…

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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eBook Problem 2-11 (Algorithmic) Let A be an event that a person's primary method of transportation to and from work is an automobile and 8 be an event that a person's primary method of transportation to and from work is a bus. Suppose that in a large city P(A) - 0.49 and P(8) -0.37. a. Are events A and B mutually exclusive? What is the probability that a person uses an automobile or a bus in going to and from work? If required, round your answer to two decimal places. b. Find the probability that a person's primary method of transportation is some means other than a bus. If required, round your answer to two decimal places. P(B) =
Problem 3 We propose another model of early propagation of an epidemic, by counting the number of indi- viduals spreading the disease as follows: At day 0, there is one person infected. From a day to the next, every infected individual independently: 1) remains a spreader with probability (w.p.) p, and has either infected exactly one new individual (who becomes a spreader) with conditional probability q, or has not spread the disease with con- ditional probability 1-q. 2) gets definitively removed from the pool of spreaders without infecting anyone else (w.p. 1-p). a. Justify why this model can be described as a branching process (what is the number of spreaders at time n + 1 given the number of spreaders at time n, what is the reproduction law). Find the generating function of the reproduction law. b. We define the contact number o as the average number of individuals directly contaminated by an infected individual before this individual is removed from the pool of spreaders. Show…
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Problem 5: A professor tries to count the number of students attending lecture in person. For each student in the audience, the professor either counts the student accurately with probability p or misses the student in the count with probability (1 – p). The exact number of attending students is 20. (a) The number of students counted by the professor is a random variable N. What is the PMF of N? (b) Let U = 20 – N denote the number of uncounted students. What is the PMF of U? (c) What is the probability that the undercount U is 2 or more? (d) For what value of p is E[U] = 2?
Discrete Mathematics Problem 2 Susie has a bag of marbles containing 3 Red, 7 Green, and 10 Blue marbles. In this problem, the phrase with replacement means that marbles are drawn one at a time and after the draw it is replaced back into the bag before picking the next marble. The phrase without replacement meansthat each marble is drawn and held onto until all marbles are drawn.1. What is the probability of picking 5 marbles and getting at least one red marble? Calculate the probability (a) with replacement, and (b) without replacement. 2. Pick 8 marbles: 4 green and 4 blue. Calculate the probability (a) with replacement and (b) without replacement. 3. If Susie sells you 7 marbles chosen randomly without replacement, what are your chances of getting at least six marbles of the same color?
Problem 14: Suppose that the checkout time at a grocery store is an exponential random variable with mean 4 minutes. Estimate the probability that a cheker will serve more than 77 customers during a 6 hour shift.
Problem 1. MIT students sometimes delay laundry for a few days. Assume all random values described below are mutually independent. (a) A busy student must complete 3 problem sets before doing laundry. Each problem set requires 1 day with probability 2/3 and 2 days with probability 1/3. Let B be the number of days a busy student delays laundry. What is E [B]? Example: If the first problem set requires 1 day and the second and third problem sets each require 2 days, then the student delays for B = 5 days.
A rat is put into the following maze: moves. 3 flat 1 The rat has a probability of 1/4 of starting in any compartment and suppose that the rat chooses a passageway at random when it makes a move from one compartment to another at each time. Let Xn be the compartment occupied by the rat after n 2 (d) Find the probability that the rat is in compartment 3 after two moves. (e) In the long run, how many times that the rat enters in compartment 4 in 100 movements?
Question C

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