Find the probability density function, Mathematics

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.

 

Posted Date: 3/22/2013 3:09:16 AM | Location : United States







Related Discussions:- Find the probability density function, Assignment Help, Ask Question on Find the probability density function, Get Answer, Expert's Help, Find the probability density function Discussions

Write discussion on Find the probability density function
Your posts are moderated
Related Questions


what does 4/100+1/10=

find the no of solution of 2*3*4*5*6*6

Now we start solving constant linear, coefficient and second order differential and homogeneous equations. Thus, let's recap how we do this from the previous section. We start alon


A circle is inscribed in a triangle ABC having sides 8cm, 10cm and 12cm as shown in the figure. Find AD, BE and CF.


Harmonic mean It is a measure of central tendency which is utilized to determine the average increase rates for natural economies. This is defined like the reciprocal of the a

What is Multiplying Fractions ? The rule for multiplying fractions is to "multiply across": Multiply the numerators to get the numerator of the answer. Multiply the den