A system consists of two components connected in series The system will fail when either of the two components fails Let T be the time at which the system fails Let X1 and X2 be the lifetimes of the two components Assume that X1 and X2 are independent and that each has theWeibull distribution with 2 and 0 2 a Find P(X1 5) b Find P(X1 5 and X2 5) c Explain why the event T 5 is the same as the event X1 5 and X2 5 d Find P(T 5) e Let t be any positive number Find P(T t), which is the cumulative distribution function of T f Does T have a Weibull distribution If so, what are its parameters

Question: A system consists of two components connected in series. The system will fail when either of the two components fails. Let T be the time

A system consists of two components connected in series. The system will fail when either of the two components fails. Let T be the time at which the system fails. Let X1 and X2 be the lifetimes of the two components. Assume that X1 and X2 are independent and that each has theWeibull distribution with α = 2 and β = 0.2.
a. Find P(X1 > 5).
b. Find P(X1 > 5 and X2 > 5).
c. Explain why the event T > 5 is the same as the event {X1 > 5 and X2 > 5}.
d. Find P(T ≤ 5).
e. Let t be any positive number. Find P(T ≤ t), which is the cumulative distribution function of T .
f. Does T have a Weibull distribution? If so, what are its parameters?

Step by Step Solution

★★★★★

3.51 Rating (161 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a PX 1 5 1PX 1 5 11e0252 e 1 03679 b Since X 2 has the same distribution as X 1 PX 2 5 PX 1 5 e ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

944-S-J-P-D (2185).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

A system consists of two subsystems connected in series, as shown in the following schematic illustration. Each subsystem consists of two components connected in parallel. The AB subsystem fails when...

A system consists of two components. The probability that the second component functions in a satisfactory manner during its design life is .9, the probability that at least one of the two components...

An electronic system is made up of two components connected in parallel. Consequently, the system fails only when both of the components fail. The probability the first component fails is 0.05 and,...

1. (a) Y1,Y2, ..., Yn form a random sample from a probability distribution with cumu- lative distribution function Fy(y) and probability density function fy(y). Let Y(1) = min{Y, Y2, ..., Yn}. Write...

The task in this design project is to design an actuation system to power the ram's reciprocating motion in a small-size shaper. The power source of the actuation system is an AC motor with 0.75 hp...

(5) 5. A system consists of three components connected a) in series ; b) in parallel. Suppose that i-th component has a lifetime that is exponentially distributed with A; = .01, A2 = .02 and A3 =...

(5) l. A system consists of three components connected so that at least 2 components must operate for the system to operate properly, i.e. this is 2-out-of-3 system (see p. 137 # 99). Suppose that...

2.2. A system consists of two components operating in parallel: The system functions if at least one of the components is operating. In any single period, if both components are operating at the...

4.2.2 A system consists of two components operating in parallel: The system functions if at least one of the components is operating. In any single period, if both components are operating at the...

Write z = rei(, where 0 when 0 rsin cose2 r sin ne 1-2r cos + r2

There are a lot of factors that come into play when choosing how to structure an organization. The buzz today seems to be around flattening organizations, implementing teams, and focusing on core...

In responsibility income statements, costs that change in approximate proportion to changes in a responsibility center's sales volume are identified as:

What are the other means available to the government for raising seigniorage revenues besides resorting to increas- ing the notes in circulation?

Particles are a major component of air pollution in many areas. It is of interest to study the sizes of contaminating particles. Let X represent the diameter, in micrometers, of a randomly chosen...

The lifetime of a certain component, in years, has probability density function. Two such components, whose lifetimes are independent, are available. As soon as the first component fails, it is...

Refer to Exercise 18.a. Find Cov(X, Y).b. Find X,Y .c. Find the conditional probability density function f Y |X (y | 0.5).d. Find the conditional expectation E(Y | X = 0.5). Refer to Exercise 18. 3...

Question 2a Based on previous research, the investigators have also predicted that the average total time at work in the last week (mins) is lower for males than for females. Conduct an independent...

Name: 9) How many paths are there from A to B if you can only move right and down? A

i just need a worked out solution of this Evaluate ji kak