An electronic control system contains 10 components that work independently of one another, and is capable...
An electronic control system contains 10 components that work independently of one another, and is capable of working normally if at most two components fail. Due to unfavorable climate conditions, each component has a failure probability of 20%. What is the probability that the system as a whole works?
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An electronic control system contains 10 components that work
independently of one another, and is capable...
Question 4 [20 marks] A system consists of five components in two branches as shown in...
Question 4 [20 marks] A system consists of five components in two branches as shown in the following diagram: C-D-E- In other words, the system works if components A and B work or components C, D, and E work. Assume that the components fail independently with the following probabilities: P(A fails) = P(B fails) = 0.1 and P(C fails) = P(D fails) = P(E fails) = 0.2. (a) What is the probability that the system works? (b) Given that the...
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...
A circuit system is given in the following figure, where the number in each component represents...
A circuit system is given in the following figure, where the number in each component represents the probability that the component works. Assume the components fail independently. (a) What is the probability that the entire system work? (b) Given that the system works, what is the probability that the component A is not working? 0.7 0.7 0.8 0.8 0.8
upposea components of system all act independently, and each fails within a year 10% of the...
upposea components of system all act independently, and each fails within a year 10% of the time Find the probability none fails within a year Find the probability at least one fails within a year Find the probability all fail within a year. Find the probability at least one works the entire year.
Suppose 4 components of system all act independently, and each fails within a year 10% of...
Suppose 4 components of system all act independently, and each fails within a year 10% of the time. Find the probability none fails within a year Find the probability at least one fails within a year Find the probability all fail within a year. Find the probability at least one works the entire year.
A system consists of three components A, B and C, which fails independently with probabilities 0.2,...
A system consists of three components A, B and C, which fails
independently with probabilities 0.2, 03 and 0.2. Let X be the
total number of failed components.
(a) Find the probability distribution of X.
(b) What is the probability that at least one component is
working.
(c) Find E(X^3 − 1).
3. (7 points) A system consists of three components A, B and C, which fails independently with probabilities 0.2, 03 and 0.2. Let X be the total number...
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,...
of components connected as in the Consider the system accompanying picture. Components 1 and 2 are...
of components connected as in the Consider the system accompanying picture. Components 1 and 2 are connected in parallel, so that subsystem works if and only it either 1 or 2 works; since 3 and 4 are connected in series, that subsystem works if and only if both 3 and 4 work. If components work independently of one another and p(component i works)-0.84 for ,-1, 2 and-0.7 for i-3, 4, calculate Pisystem works). (Round your answer to tour decimal places.)...
Consider the system of components connected as in the accompanying picture. Components 1 and 2 are...
Consider the system of components connected as in the
accompanying picture. Components 1 and 2 are connected in parallel,
so that subsystem works if and only if either 1 or 2 works; since 3
and 4 are connected in series, that subsystem works if and only if
both 3 and 4 work. If components work independently of one another
and P(component i works) = 0.73 for
i = 1, 2
and = 0.65 for
i = 3, 4,
calculate P(system...
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...
Question 4 [20 marks] A system consists of five components in two branches as shown in the following diagram: C-D-E- In other words, the system works if components A and B work or components C, D, and E work. Assume that the components fail independently with the following probabilities: P(A fails) = P(B fails) = 0.1 and P(C fails) = P(D fails) = P(E fails) = 0.2. (a) What is the probability that the system works? (b) Given that the...
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...
A circuit system is given in the following figure, where the number in each component represents the probability that the component works. Assume the components fail independently. (a) What is the probability that the entire system work? (b) Given that the system works, what is the probability that the component A is not working? 0.7 0.7 0.8 0.8 0.8
upposea components of system all act independently, and each fails within a year 10% of the time Find the probability none fails within a year Find the probability at least one fails within a year Find the probability all fail within a year. Find the probability at least one works the entire year.
Suppose 4 components of system all act independently, and each fails within a year 10% of the time. Find the probability none fails within a year Find the probability at least one fails within a year Find the probability all fail within a year. Find the probability at least one works the entire year.
A system consists of three components A, B and C, which fails
independently with probabilities 0.2, 03 and 0.2. Let X be the
total number of failed components.
(a) Find the probability distribution of X.
(b) What is the probability that at least one component is
working.
(c) Find E(X^3 − 1).
3. (7 points) A system consists of three components A, B and C, which fails independently with probabilities 0.2, 03 and 0.2. Let X be the total number...
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,...
of components connected as in the Consider the system accompanying picture. Components 1 and 2 are connected in parallel, so that subsystem works if and only it either 1 or 2 works; since 3 and 4 are connected in series, that subsystem works if and only if both 3 and 4 work. If components work independently of one another and p(component i works)-0.84 for ,-1, 2 and-0.7 for i-3, 4, calculate Pisystem works). (Round your answer to tour decimal places.)...
Consider the system of components connected as in the
accompanying picture. Components 1 and 2 are connected in parallel,
so that subsystem works if and only if either 1 or 2 works; since 3
and 4 are connected in series, that subsystem works if and only if
both 3 and 4 work. If components work independently of one another
and P(component i works) = 0.73 for
i = 1, 2
and = 0.65 for
i = 3, 4,
calculate P(system...
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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