Question

In: Statistics and Probability

An engineering system consisting of n components is said to be a k-out-of-n system (k ≤...

An engineering system consisting of n components is said to be a k-out-of-n
system (k ≤ n) if the system functions 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 Pi , i=1, 2, 3, 4, compute
the probability that a 2-out-of-4 system functions.
(b) Repeat (a) for a 3-out-of-5 system.

Solutions

Expert Solution


Related Solutions

Engineering system of type k-out-of-n is operational if at least k out of n components are...
Engineering system of type k-out-of-n is operational if at least k out of n components are operational. Otherwise, the system fails. Suppose that a k-out-of-n system consists of n identical and independent elements for which the lifetime has Weibull distribution with parameters r and λ. More precisely, if T is a lifetime of a component, P(T ≥ t) = e−λtr, t ≥ 0. Time t is in units of months, and consequently, rate parameter λ is in units (month)−1. Parameter...
a) A k-out-of-n system is one that will function if and only if at least k...
a) A k-out-of-n system is one that will function if and only if at least k of the n individual components in the system function. If individual components function independently of one another, each with probability 0.8, what is the probability that a 4-out-of-6 system functions? b) Obtain ?(?(?−2)) where ? ~???????(?) c) Service calls arrive at a maintenance center according to a Poisson process, with average 3.1 calls per minute. (i) Obtain the probability that no more than 4...
A system consisting of two components is subject to a series of shocks that arrive according...
A system consisting of two components is subject to a series of shocks that arrive according to a Poisson process with a rate of one per day. Half the shocks cause no damage, one in ten damages component 1 alone, one in five damages component 2 alone, and the rest damage both components. Note that if only one component is functioning, and a shock occurs that would damage both components, the functioning component is damaged. Compute the probability that the...
Let S_k(n) = 1^k + 2^k + ··· + n^k for n, k ≥ 1. Then,...
Let S_k(n) = 1^k + 2^k + ··· + n^k for n, k ≥ 1. Then, S_4(n) is given by S_4(n)= n(n+1)(2n+1)(3n^2 +3n−1)/ 30 Prove by mathematical induction.
Part 1 Systems engineering is said to be a disciplined process. Why do system failures still...
Part 1 Systems engineering is said to be a disciplined process. Why do system failures still occur? Choose an example of a technology or system failure (Examples: early airbags, Titanic, Challenger or Columbia disasters). Then respond to the following in discussion: Explain reasons for the failure. Use figures and/or other visual aids to explain your answer. Identify and explain any system acquisition processes that were not followed that may have contributed to the failure. You may also use your own...
The production function is f(K,N) = N/2 + √ K, where N is the amount of...
The production function is f(K,N) = N/2 + √ K, where N is the amount of labor used and K the amount of capital used. (a) What is returns to scale of this production function? What is the marginal product of labor? (b) In the short run, K¯ = 4. Labor is variable. On the graph, draw output as a function of labor input in the short run in blue. Draw the marginal product of labor as a function of...
A system with m = 0.010 kg , k = 36 N/m and b = 0.5...
A system with m = 0.010 kg , k = 36 N/m and b = 0.5 kg/s is driven by a harmonically varying force of amplitude 3.6 N. Find the amplitude A and the phase constant δ of the steady-state motion when the angular frequency of the driving force is : a) 8.0 rad/s, b) 80 rad/s c) 800 rad/s. *Be careful, tan(δ) is a periodic function and δ should be between 0 and 180°.
1. prove s(n, k) = s(n − 1, k − 1) − (n − 1)s(n −...
1. prove s(n, k) = s(n − 1, k − 1) − (n − 1)s(n − 1, k). 2. What is ∑n k=0 s(n, k)?
Depolarization is caused by: K+ diffusing out of the neuron K+ being pumped out of the...
Depolarization is caused by: K+ diffusing out of the neuron K+ being pumped out of the neuron Na+ being pumped into the neuron Na+ diffusing into the neuron Hyperpolarization: can be caused after neurotransmitters bind to postsynaptic neurons means the neuron’s internal environment is even more positively charged than usual can be caused by sodium ion gated channels being open each of the above is correct Typically, an unmyelinated small diameter axon would have: a faster speed of action potential...
Explain the basic components of social engineering attacks
Explain the basic components of social engineering attacks
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT