A parallel system consisting of 4 independent components works if at least one component works. However,...
- A parallel system consisting of 4 independent components works if at least one component works. However, a seriesl system consisting of 4 independent components works if all components work.
- Now suppose probability p of any component works is 0.5.
- Compute the following quantity and interpret your results.
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A parallel system consisting of 4 independent components works
if at least one component works. However,...
4. A parallel system functions whenever at least one of its components works. Suppose you have...
4. A parallel system functions whenever at least one of its components works. Suppose you have two separate parallel systems, A and B, each consisting of n identical components that work independently with probability p. a) Consider parallel system A. Given that the system is functioning, what is conditional probability that component 1 works? (This has nothing to do with B yet.) Suppose system B breaks down (all n of its components fail), but system A remains functional. To get...
8 (10 polints) A ystem conslists of 4 components ln a eries, so the system works properly if all of the for 1- 1,2,3,4 components are functional. In other words, the system fails if and only I...
8 (10 polints) A ystem conslists of 4 components ln a eries, so the system works properly if all of the for 1- 1,2,3,4 components are functional. In other words, the system fails if and only If at least one of its components als Suppose the probability that the component falils is less than or equal to p Flad n pper bound on the probability that the syetem fails 6. (10 points) A system consists of 4 components in a...
Problem 4 Consider the system of components connected as depicted below. The system can be thought...
Problem 4 Consider the system of components connected as depicted below. The system can be thought of as being comprised of two subsystems: one with components A and B, and the other with components C and D. Components A and B are connected in parallel, therefore that subsystem works iff either A or B works. Since C and D are connected in series, that subsystem works iff both C and D work. Components work independent of each other (that is,...
(5) 5. A system comprised of three independent components. The probability of failure for each component...
(5) 5. A system comprised of three independent components. The probability of failure for each component is given. (Use our standard notation: Ai, i 1,2,3; A.) #1 .1 #2 .2 #3 .3 a) Find the probability that the system works - [A]. b) Find the probability that exactly one component works B c) Find the probability that at least one component works [C.
2, (20%) A particular operation has six components. Each component has a failure probability q, independent of any othe...
2, (20%) A particular operation has six components. Each component has a failure probability q, independent of any other component. The operation is successful if both of the following conditions hold: Component 1, 2, and 3 all work, or component 4 works. Either component 5 or component 6 works. The block diagram of this operation is shown below. b. (10%) Suppose we can replace one of the components with a more reliable component that has failure probability of q/2 Which...
Consider purchasing a system of audio components consisting of a receiver, a pair of speakers, and...
Consider purchasing a system of audio components consisting of a receiver, a pair of speakers, and a CD player. Let A, be the event that the receiver functions properly throughout the warranty period, A, be the event that the speakers function properly throughout the warranty period, and A, be the event that the CD player functions properly throughout the warranty period. Suppose that these events are (mutually) independent with P(A) = 0.91, P(A) = 0.92, and P(A3) = 0.90. (Round...
5. A system consisting of n components is said to be a k-out-of-n system (ksn) if...
5. A system consisting of n components is said to be a k-out-of-n system (ksn) if the system functions during a given mission time if and only if at least k of the n components function. Suppose that all components function independently of each other. a) If the ith component functions with probability P, i-1,2,3 derive the formula for the probability that a 2-out-of-3 system functions. b) Repeat part a) for a 3-out-of-4 system. c) Calculate the probability that the...
84. Consider purchasing a system of audio components consisting of a receiver, a pair of speakers,...
84. Consider purchasing a system of audio components consisting of a receiver, a pair of speakers, and a CD player. Let A be the event that the receiver functions properly throughout the warranty period, Ay be the event that the speakers function properly throughout the warranty period, and A, be the event that the CD player functions properly throughout the warranty period. Suppose that these events are (mutually) independent with P(A)95, P(A2) .98, and P(As) 80. a. What is the...
Part c (6) 6. A system comprised of three independent components. The probability of failure for...
Part c
(6) 6. A system comprised of three independent components. The probability of failure for each component is given. (Use our standard notation: Ai, i 1,2, 3; A.) #1 .1 #3 .3 a) Find the probability that the system works (A). b) Find the probability that at least one component works (B e) Find the probability that the system works, given that at least one component wor ks.
A system of comprised of three independent components. The probability of failure for each component is...
A system of comprised of three independent components. The
probability of failure for each component is given,
D4 MORE NON-CAR (6) 3. A system comprised of thrce independent components. The probability of failure for each component is given. #2.2 #3.3 #1 .1 Use our standard Noration: A,, A2, A3, A [system operates properly) a) Find the probability that the system operates properly. b) Find the probability that at most two of the components work. (event B) c) Find the probability...
4. A parallel system functions whenever at least one of its components works. Suppose you have two separate parallel systems, A and B, each consisting of n identical components that work independently with probability p. a) Consider parallel system A. Given that the system is functioning, what is conditional probability that component 1 works? (This has nothing to do with B yet.) Suppose system B breaks down (all n of its components fail), but system A remains functional. To get...
8 (10 polints) A ystem conslists of 4 components ln a eries, so the system works properly if all of the for 1- 1,2,3,4 components are functional. In other words, the system fails if and only If at least one of its components als Suppose the probability that the component falils is less than or equal to p Flad n pper bound on the probability that the syetem fails 6. (10 points) A system consists of 4 components in a...
Problem 4 Consider the system of components connected as depicted below. The system can be thought of as being comprised of two subsystems: one with components A and B, and the other with components C and D. Components A and B are connected in parallel, therefore that subsystem works iff either A or B works. Since C and D are connected in series, that subsystem works iff both C and D work. Components work independent of each other (that is,...
(5) 5. A system comprised of three independent components. The probability of failure for each component is given. (Use our standard notation: Ai, i 1,2,3; A.) #1 .1 #2 .2 #3 .3 a) Find the probability that the system works - [A]. b) Find the probability that exactly one component works B c) Find the probability that at least one component works [C.
2, (20%) A particular operation has six components. Each component has a failure probability q, independent of any other component. The operation is successful if both of the following conditions hold: Component 1, 2, and 3 all work, or component 4 works. Either component 5 or component 6 works. The block diagram of this operation is shown below. b. (10%) Suppose we can replace one of the components with a more reliable component that has failure probability of q/2 Which...
Consider purchasing a system of audio components consisting of a receiver, a pair of speakers, and a CD player. Let A, be the event that the receiver functions properly throughout the warranty period, A, be the event that the speakers function properly throughout the warranty period, and A, be the event that the CD player functions properly throughout the warranty period. Suppose that these events are (mutually) independent with P(A) = 0.91, P(A) = 0.92, and P(A3) = 0.90. (Round...
5. A system consisting of n components is said to be a k-out-of-n system (ksn) if the system functions during a given mission time if and only if at least k of the n components function. Suppose that all components function independently of each other. a) If the ith component functions with probability P, i-1,2,3 derive the formula for the probability that a 2-out-of-3 system functions. b) Repeat part a) for a 3-out-of-4 system. c) Calculate the probability that the...
84. Consider purchasing a system of audio components consisting of a receiver, a pair of speakers, and a CD player. Let A be the event that the receiver functions properly throughout the warranty period, Ay be the event that the speakers function properly throughout the warranty period, and A, be the event that the CD player functions properly throughout the warranty period. Suppose that these events are (mutually) independent with P(A)95, P(A2) .98, and P(As) 80. a. What is the...
Part c
(6) 6. A system comprised of three independent components. The probability of failure for each component is given. (Use our standard notation: Ai, i 1,2, 3; A.) #1 .1 #3 .3 a) Find the probability that the system works (A). b) Find the probability that at least one component works (B e) Find the probability that the system works, given that at least one component wor ks.
A system of comprised of three independent components. The
probability of failure for each component is given,
D4 MORE NON-CAR (6) 3. A system comprised of thrce independent components. The probability of failure for each component is given. #2.2 #3.3 #1 .1 Use our standard Noration: A,, A2, A3, A [system operates properly) a) Find the probability that the system operates properly. b) Find the probability that at most two of the components work. (event B) c) Find the probability...
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