5. A system consisting of n components is said to be a k-out-of-n system (ksn) if...
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...
Question 2 (6 points) A system contains two components, A and B, connected in series, as shown in the diagram. Assume A and B function independently. For the system to function, both components must function. a. If the probability that A fails is 0.05, and the probability that B fails is 0.03, b. If both A and B have probability p of failing, what must the value of pbe so c. If three components are connected in series, and each...
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...
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...
Consider a system consisting of three components as pictured. The system will continue to function as long as the first component functions and either component 2 or component 3 functions. Let X1, X2, and X3 denote the lifetimes of components 1, 2, and 3, respectively. Suppose the Xi's are independent of one another and each X, has an exponential distribution with parameter λ. (a) Let Y denote the system lifetime. Obtain the cumulative distribution function of Y and differentiate to...
5. A communication system consists of n components each of which will function indepen- dently with probability p. The total system will operate effectively if at least half of its components function. (a) What is the probability that the total system will operate effectively if n = 3? (b) What is the probability that the total system will operate effectively if n = 5? (c) For what values of p will & 5-component system be more likely to operate effectively...
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...
SHOW ALL WORK! PROBLEM 3.2 (pg 87, #80-see diagrann below) Consider the system of components in the accompanying picture. Components 3 and4 are connected in series (call this subsystem 3-4). Subsystem 3-4 will work only if both components 3 and 4 work. In order for the entire system to function, it must be the case that component 1 functions (Ai) or component 2 functions (A2) or that subsystem 3-4 functions (A34). Suppose that each individual component functions independently of all...
Suppose a system of ive components Ai,1 Si S 5 is arranged as follows 2 Assum e the lifetime of each component is exponentially distributed with parameter) and the components function independently. Let of the i-th component, that is the random variable defined by (Xi - t) means that the the i-th component stops working at time t. Saying that Xi has an exponenti distribution with parameter X means X, be the lifetime random variable and P(Xi s t)-1-e*. be...
Hello, I need help for this problem. A system is composed of N identical components. Each independently operates a random length of time until failure. This failure time is exponential with rate λ. When a component fails, it undergoes repair. The repair time is random, exponential with rate µ. The system is said to be in state n at time t if there are exactly n components under repair at time t. This process is a birth and death process....