Problems1. Consider an database server designed to handle a maximum of 15 transactionsper second. During the peak hour of its activity, transactions arrive at the averagerate of 10 per second (10 s ¹). Assuming that the number of transactions arrivingper second follows a Poisson distribution, compute the probability that the serverwill be overloaded during a peak hour.

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Answered: Problems 1. Consider an database server…

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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I'm mainly struggling to understand part C
(b) Ali Baba's Car Wash Service Centre is open 6 days a week, but its busiest day is always on Sunday. From the previous data, Ali Baba estimates that dirty cars arrive at the rate of one every two minutes. One car at a time is cleaned in this example of a single-channel waiting line. Assuming Poisson arrivals and exponential service times, find the following: [Pusat Servis Cuci Kereta Ali Baba dibuka 6 hari seminggu, tetapi hari yang paling sibuk selalunya pada hari Ahad. Daripada data yang lepas, Kedai Cuci Kereta Ali Baba menganggarkan bahawa kereta kotor tiba pada kadar satu setiap dua minit. Satu kereta pada satu masa dibersihkan dalam contoh saluran menunggu satu saluran ini. Dengan andaian ketibaan tahuran Poisson dan masa perkhidmatan eksponensial, carikan yang berikut:] i) Compute the average number of cars in line. [Kirakan purata untuk bilangan kereta yang menunggu dalam baris.) ii) Calculate the value of probability that there are no car in the system. [Kirakan nilai…
.A new, miracle diabetes drug that diminishes major symptoms of diabetes has been approved by the FDA. Health care professionals and researchers believe that the new drug will prolong lifespan of diabetes patients. If the population is in steady state and the incidence is constant, what will the effect of this new drug be on the prevalence of diabetes in the population? Explain.
Working problem 4.12: If the event is a number '5' tuming in rolling a die, simulate rolling a die for 1000 times with increments of 100 and explain how the law of large numbers will prevail. Working problem 4.13 : The data in the Table below was taken from the U.S. Census Bureau report titled "HINC-01. Selected Characteristics of Households, by Total Money Income in 2005" (http://www.census.gov/hhes www/cpstables/032010/hhinc/new01 001.htm) Income Under $20,000 $20,000 to < $40.00O $40,000 to < $60.00O S60,000 to < $80,000 $80,000 to < $100,000 Above $100,000 Households (thousands) 24,559 26,904 20.026 14,535 9,362 7,813 If a U.S. family is selected at random, Determine (a) The probability that the family selected has an annual income of less than $40,000 (b) The probability that the family selected has an annual income of $40,000 to less than $80,000 (c) The probability that the family selected has an annual income of more than $100,000 29
Consider a set of three assets, one risk-free and two risky. The covariance matrix [0.36 0.07] for the risky assets is given by = 0.07 The risk-free rate is 0.03 0.07 0.29 and risk aversion is A = 4. Calculate the optimal portfolio for this individual.
5. Consider an ensemble of three single-point-of-failure components. The lifetime of the first component has an exponential distribution with parameter 0.001 failures per hour. The lifetime of the second component has a Weibull distribution with parameters 0.001 and 1.7, and the lifetime of the third component has a lognormal distribution with parameters 0.005 and 2.3. If the components are considered stochastically independent, what is the probability that the ensemble survives at least 40,000 hours? What information would be required to solve this problem if the components are not considered stochastically independent?
1. Suppose that for a stochastic variable X~B(n;p) with the parameters n =10 and p = 30% a) BY HAND (PICTURE MUST BE UPLOADED): Calculate the mean and the standard deviation b) Use IT to determine P(X = 4).
Consider an investor borrowing at the risk free rate and investing a share of his wealth greater than one in the market portfolio. The beta of this investor’s portfolio is Equal to one Smaller than one Larger than one Equal to zero
The lifetime of a bulb is modeled as a Poisson variable. You have two bulbs types A andB with expected lifetime 0.25 years and 0.5 years, respectively. When a bulb’s life ends, it stops working. You start with new bulb of type A at the start of the year. When it stopsworking, you replace it with a bulb of type B. When it breaks, you replace with a type Abulb, then a type B bulb, and so on.1. Find the expected total illumination time (in years), given you do exactly 3 bulb re-placements2. Your replacements are now probabilistic. If your current bulb breaks, you replaceit with a bulb of type A with probability p, and with type B with probability (1 –p). Find the expected total illumination time (in years), given you do exactly n bulbreplacements, and start with bulb of type A

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