77. A system consists of five identical componentsconnected in series as shown:1345As soon as one component fails, the entire systemwill fail. Suppose each component has a lifetimethat is exponentially distributed with 2 = .01 andthat components fail independently of oneanother. Define events A; :at least t hours }, i = 1, ... , 5, so that the A;'s areindependent events. Let X = the time at which thesystem fails- that is, the shortest (minimum)lifetime among the five components.a. The event {X > t} is equivalent to what eventinvolving A1, ..., As?b. Using the independence of the five A;'s, com-pute P(X > t). Then obtain F(t) = P(X < 1)and the pdf of X. What type of distribution{ith component lastsdoes X have?c. Suppose there are n components, each havingexponential lifetime with parameter å. Whattype of distribution does X have?

Given data A system consists of five identical components connected in series shown in fig if the…

Answered: 77. A system consists of five identical…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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3) A light fixture contains five lightbulbs. The lifetime of each bulb is exponentially distributed with mean 200 hours. Whenever a bulb burns out, it is replaced. Let T be the time of the first bulb replacement. Let Xi, i = 1, . . . , 5, be the lifetimes of the five bulbs. Assume the lifetimes of the bulbs are independent.
The table shows the leading causes of death in a certain country in a recent year. The population of the country was 311311 million. If you lived in a typical city of 500,000, how many people would you expect to die of cancercancer each year? Cause Deaths Cause Deaths Heart disease 596 comma 700596,700 Alzheimer's disease 84 comma 90084,900 Cancer 575 comma 300575,300 Diabetes 73 comma 40073,400 Chronic respiratory diseases 143 comma 100143,100 Pneumonia/Influenza 53 comma 40053,400 Stroke 128 comma 600128,600 Kidney disease 45 comma 30045,300 Accidents 122 comma 500122,500 Suicide 38 comma 60038,600 About people would be expected to die of cancer each year. (Type a whole number. Round to the nearest person as needed.)
Suppose a coin with Pr[H] = 2/3 is flipped 3 times. Using a tree, find the probability that heads was flipped two of the three times.
5. A pet food company randomly chooses two groups of 20 puppies for a study. One group eats a new brand of dog food and the other group eats an off-brand dog food for a period of 4 weeks. Researchers record muscular and skeletal growth rates in both groups. What type of study is being described?
Assume that the batter hits with probability 0.2 against left-handed pitchers, and with probability 0.3 against right-handed pitchers. Both situations are Bernoulli processes. One month the player bats 22 times against left-handed pitchers and 52 times against right-handed pitchers. How many hits should the batter expect to get during this month?
6. A small company can employ 3 workers. Each worker independently stays on the job for an exponentially distributed time with a mean of one year and then quits. When a worker quits, it takes the company an exponentially distributed time with a mean of 1/10 of a year to hire a replacement for that worker (independently of how long it takes to replace other workers). If the company takes in $1000 per day in revenue when it has 3 workers, $800 per day when it has 2 workers, and $500 per day when it has 0 or 1 workers, what is the company's long-run average daily revenue?
116. For a device to work properly, three subsystems of the device must all function properly. To increase the reliability of the device, spare units may be added to each system. It costs 100 TL to add a spare unit to system 1, 300 TL to system 2, and 200 TL to system 3. As a function of the number of added spares (a maximum of two spares may be added to each system), the probability that each system will work is given in Table. Use dynamic programming to maximize the probability that the device will work properly, given that 600 TL is available for spare units. Identify and explain decision variables, stages, states and formulate a recursion to design the device with optimal reliability. Probability that a system works system 1 Number of spares system 3 system 2 .60 .85 .70 1 .90 .85 .90 2 .95 .95 .98 117. You are planning on moving to a new house. You need to move n items of size aj , j-1,2,.,.n. You have bought m boxes (box i has size bi , i- 1,2,.,m). You need to rent a truck that…
1. There are at most 35 children and adult in a bus. Each child paid 100 pesos and an adult 150 pesos respectively. If the total amount collected was not more than 4,700 pesos. How many children and adults are there?
The complement of an event is all possible outcomes not in the event. For example: If A = at least 3 girls are born to a family with 6 kids. Then A' = A compliment is what happens if there are not at least 3 girls = less than 3 girls born to the family. A useful formula: P(A) + P(A' ) = 1 or P(A') = 1 - P(A). If P(A) = 0.194, what is P(A')?
If the life expectacy in county A is 65 years with CI of (55, 75) and in county B is 87 years with CI of (40, 98), are the two life expectancies likely to be statistically different?

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