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
((1/x^1/2-(x-1)^1/2)+(1/(5-3(x-1)^2)^1/2)

State DeMorgan's law. Prove it using the truth table.   Ans: DeMorgan's law defines that    (i)  (x ∨ y)' = x' ∧ y' (ii)  (x ∧ y)' = x' ∨ y'      Now let us dr


Here, we have tried to present some of the different thinking and learning processes of preschool and primary school children, in the context of mathematics learning. We have speci

write as a percent 6/10

Definition: An equation is considered as function if for any x in the domain of the equation (the domain is the entire x's which can be plugged into the equation) the equation wil

A number, x, increased through 3 is multiplied by the similar number, x, increased by 4. What is the product of the two numbers in terms of x? The two numbers in terms of x wou

Example of quotient rule : Let's now see example on quotient rule.  In this, unlike the product rule examples, some of these functions will require the quotient rule to get the de

Graph for the Sequence First we wish to think about the term graphing a sequence. To graph the sequence {a n } we plot the points {n, a n } as n ranges over every possible valu

450 girls were surveyed about their favorite sport, 24% said in which basketball is their favorite sport, 13% said in which ice hockey is their favorite sport, and 41% said which s