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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A club recruit member either through active recruitment by its current members or through advertising in neighborhood billboards. Suppose that each member of the club recruit new members at a rate of 3 members per week and that advertising in neighborhood billboards generate new members at a rate of 2 members per week. Suppose further that each member is expected to stay a club member for 1 week, on average. Assume that the number of members of the club at any given time follows a birth and death process. Given that the club started with 5 members, what is the expected number of club members after the first two weeks? (Hint: refer to the theorem below) Theorem For a linear growth process with immigration and Xo = i, we have 0 · (e(x-μ)t - 1) + ie(x-μ)t, x‡μ E (X₂) = x-fl Ot + i, λ = μ.
1.Suppose that one word is to be selected at random from the sentence "THE GIRL PUT ON HER BEAUTIFUL RED HAT". If X denotes the number of letters in the word that is selected, (1) What is the value of E(X)? (2) What is the value of Var(X)?
On each trial of an experiment, a subject is presented with a constant soft noise, which is interrupted at some unpredictable time by a noticeably louder sound. The time it takes for the subject to react to this louder sound is recorded. The following list contains the reaction times (in milliseconds) for the 16 trials of this experiment: 285, 175, 164, 217, 273, 222, 212, 202, 236, 229, 171, 235, 193, 186, 261, 241 Send data to calculator th Find 40" and 75" percentiles for these reaction times. (a) The 40 th percentile: || milliseconds (Ь) The 75 th percentile: milliseconds
A group of researchers wishes to see if the total number of diseases that occurred in six countries are the same. The data are shown in the table. At α = 0.05 is there enough evidence to reject the claim that the number of diseases in the six countries are the same? Philippines - 8,6,7,10,16 India -6,13,16,10,7 Thailand. -5,8,16,22,12 Singapore. -14,12,8,9,15 Korea. -5,4,32,21,17 Japan. -6,18,15,24,16
(3.) A system contains components connected in parallel as shown in the diagram. If all components operate inderentently, & each component has probability 0.45 of failing What is the minimum number of components that must be connected in parallel so that th Probability that the system operateds exceeds 0.9999? The minimun number of components that must be connected in parallel is.
1. The events A and B are such that P(A) = 1/3, P(A'|B) = ¼/4, and P(AUB) = ½. Find a) P(A'nB). Ans: 1/6 b) P(B). Ans: 2/3
PROBABILITY UPVOTE WILL BE GIVEN. PLEASE WRITE THE COMPLETE SOLUTIONS. ANSWER IN 4 DECIMAL PLACES. Determine the following: a. Determine the number of probabilities of getting exactly 4 fives when a certain die is tossed 8 times. b. The probability that you will pass Differential Equation is 0.3. If you have 5 friends in your circle including you, what is the probability that at most 2 are accepted?
Suppose X-U (-54, 60) and F(t) is the cumulative distribution function. What is the probability that X is in the interval [-51, -21] or in the interval [-36, 57]? O (F(-21)-F(-51))+ (F(57) - F(-36)) O (F(-21)-F(-51)) x (F(57) - F(-36)) O F(-21)-F(-36) O F(57) - F(-51)
6.
A golfer practices different parts of their game for hours. Specifically, the golfer practices:(1) putting, (2) their short game, and (3) their iron game. The amount of time spent on each partof their game is exponentially distributed. If the golfer is practicing their putting, they will alwaysswitch to their short game after an average of 30 minutes. When the golfer practices their short game,they do so for an average of 45 minutes, and then switches to putting with probability 0.6 or to theiriron game with probability 0.4. When they practice their iron game, they do so for an average of 60minutes. After practicing their iron game, the golfer will switch to putting or to their short game withequal probability.(a) Draw the CTMC rate diagram, clearly label your states and transition rates (qij ’s)(b) Find the transition rates out of the states (vi’s) and transition probabilities (Pij ’s).(c) Find the limiting probabilities (make sure to write out the balance equations).(d) In the long…
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')?
On each trial of an experiment, a participant is presented with a constant soft noise, which is interrupted at some unpredictable time by a slightly louder sound. The time it takes for the participant to react to the louder sound is recorded. The following list contains the reaction times (in milliseconds) for 26 trials of this experiment. 156, 202, 214, 222, 234, 250, 279, 280, 280, 297, 298, 299, 301, 303, 311, 329, 340, 358, 373, 394, 419, 436, 451, 583, 701, 864 Send data to Excel Aa Frequency 12 12- 10 10- 8- 6. 4. 2 2- 150 300 450 600 750 1000 Reaction time (in milliseconds)

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