1) Find as an algebraic expression the mean life of a parallel system with two components, each of which has an exponential life distribution with hazard rate λ1 & λ2 respectively. 1) Find a...
1) Find as an algebraic expression the mean life of a parallel system with two components, each of which has an exponential life distribution with hazard rate λ1 & λ2 respectively. 1) Find as an algebraic expression the mean life of a parallel system with two components, each of which has an exponential life distribution with hazard rate λ1 & λ2 respectively.
1) Find as an algebraic expression the mean life of a parallel system with two components, each of which has an exponential life distribution with hazard rate λ1 & λ2 respectively. 1) Find as an algebraic expression the mean life of a parallel system with two components, each of which has an exponential life distribution with hazard rate λ1 & λ2 respectively.
Q. 2 (Gamma and exponential, 30 pts). A parallel system consists of two components with independent lifetimes. The lifetime Ly of the first component is memoryless: it has the exponential distribution with parameter 1. On the other hand, based on statistical analyses, it is found out that the lifetime L2 of the second component has two independent phases each of which has the same characteristics as L). Therefore, it is assumed that L2 has the gamma distribution with shape index...
Consider a parallel system of n identical components, each with an exponential time to failure with mean 1/A Show that the mean time to failure of the system is given by: Hi-i.) 1l
Consider a system with n components c1, c2, …, cn which are connected in series. If the component ci has failure density that is exponential with mean θi, i = 1, 2, ..., n What is the reliability of the systemic? That is find the survival function What is the mean failure time of the system? suppose the n components are connected in parallel. Find the reliability of the system and an expression for it mean failure time
Suppose that a given individual in a population has a survival time which is exponential with a hazard rate 0. Each individual's hazard rate θ s potentially different and is sampled from a gamma distribution with density function TCB) Let X be the life length of a randomly chosen member of this popula- tion. (a) Find the survival function of X. (Hint: Find S(x) Ele" .) (b) Find the hazard rate of X. What is the shape of the hazard...
Suppose that two electronic components in the guidance system for a missile operate independently and that each has a life length governed by the exponential distribution with mean 1 (with measurements in hundreds of hours). 1 + a2Y2, then it can be shown that the If Y1 and Y2 are independent random variables with moment-generating functions my, (t) and my (t), respectively, and a, and an are constants, and U = a moment-generating function for U is my(t) = my,...
(25 points,) Let X and Y be two independent and identically distributed random variables that have exponential distribution with rates 1 respectively. Find the distribution of Note: you can give either cdf or pdf) (25 points,) Let X and Y be two independent and identically distributed random variables that have exponential distribution with rates 1 respectively. Find the distribution of Note: you can give either cdf or pdf)
Suppose we are analyzing data from the exponential distribution, which has density function f (y) = ò exp (-5y) for y > 0, depending on a single parameter δ > 0, The exponential distribution arises in reliability theory as the waiting time until failure of a system that is subject to a constant risk of failure δ. (a) Using a computer: plot f(y; δ) as a function of y when δ-1. What is the area under this curve, and why?...
28. An electronic system is composed of three components (o1. 92, and o), each of which operates independently of the other two. The electronic system has two paths available from node A to node B. C1 C2 Information is thus able to be transmitted from A to B, provided that at least one path is in operation (either 1 is operative or both o2 and c3 are in operation simultaneously). Given: P(o is in operation)0.9 P(c2 and c3 are in...