Find the probability density function, Mathematics

Assignment Help:

1. The lifetime T (in days) of an electrical component has reliability function given by: R(t) = e-0.01t for time t > 0. An electrical system consists of four such components. The system continues to function if at least one component is still 'alive' and the system is repaired (by replacing all the components) when all components have expired.

(a) Find the probability density function (PDF) of T, the lifetime of a component in the system.

(b) Show that this is a valid PDF.

(c) Find the reliability function for the system.

(d) Find the probability that the system lasts for longer than 1 year (365 days).

(e) Simulate the lifetime of the system.

(f) Set the random number seed using set.seed(1). Then simulate 20 lifetimes for the system. Calculate the sample mean lifetime of the system using your 20 simulated values.

 


Related Discussions:- Find the probability density function

Curvature, steps to trace the cartesian curve

steps to trace the cartesian curve

Example of word problem, Example of Word problem: There is a man who i...

Example of Word problem: There is a man who is 21 years older than his son.  5 years ago he was four times as old as his son. How older are both now? Solution: Step 1

Total linear attenuation, Consider the task of identifying a 1 cm thick bre...

Consider the task of identifying a 1 cm thick breast cancer that is embedded inside a 4.2 cm thick fibroglandular breast as depicted in Fig. The cancerous tumor has a cross

Commercial arithmetic, if oranges are bought at the rate of 11 for rupees ...

if oranges are bought at the rate of 11 for rupees 10 and are sold at the rate of 10 for rupees 11, find the profit percent

Estimation of difference among two means, Estimation of difference among tw...

Estimation of difference among two means We know that the standard error of a sample is given by the value of the standard deviation (σ) divided by the square root of the numbe

Infinite interval - improper integrals, Infinite Interval  - Improper Inte...

Infinite Interval  - Improper Integrals In this type of integral one or both of the limits that is upper limit and lower limit of integration are infinity.  In these cases the

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd