Question

Problem 4 (10pts). A piece of equipment has 5 independent parts at least 4 of which uust remain active ith in order for the equipment to function. The lifetine (n hours) of each component follows a distribution w probability density function 0, else. Find the probability density function of the lifetime T (in hours) of the equipment

0 0
Add a comment Improve this question Transcribed image text
Know the answer?
Add Answer to:
Problem 4 (10pts). A piece of equipment has 5 independent parts at least 4 of which...
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for? Ask your own homework help question. Our experts will answer your question WITHIN MINUTES for Free.
Similar Homework Help Questions
  • part a, b and c please Problem 4. (15 points) The probabiälity density function of X, the lifetime of a lamp (meured in i hours), Is given 10 0, s 10 (a) Find P(x>20) 3 b) What is the cumulativ...

    part a, b and c please Problem 4. (15 points) The probabiälity density function of X, the lifetime of a lamp (meured in i hours), Is given 10 0, s 10 (a) Find P(x>20) 3 b) What is the cumulative distribution fpaction of (e) What is the probability that, of 3 of these lampe, at keast 2 will function for at least 15 hours? Assume that the 3 lamps function/fail independent of each other 7 Problem 4. (15 points) The...

  • 1 (10pts) Let U1, U2, ... ,Un be independent uniform random variables over [0, 0] with...

    1 (10pts) Let U1, U2, ... ,Un be independent uniform random variables over [0, 0] with the probability density function (p.d.f). () = a 2 + [0, 03, 0 > 0. Let U(1), U(2), .-. ,U(n) be the order statistics. Also let X = U(1)/U(n) and Y = U(n)- (a) (5pts) Find the joint probability density function of (X, Y). (b) (5pts) From part (a), show that X and Y are independent variables.

  • Problem 4. Let X1, . . . , Xn be independent with common density f(x) =...

    Problem 4. Let X1, . . . , Xn be independent with common density f(x) = 2x 1[0 < x < 1]. Set Vn = max(X1, . . . , Xn). . (b) Show that n(1 − Vn) → W in D holds for some random variable W and find the distribution function of W

  • Problem No. 4 / 10 pts. Given The lifetime, in years, of a certain type of...

    Problem No. 4 / 10 pts. Given The lifetime, in years, of a certain type of pump is a random variable with probability density function 0 True (a) What is the probability that a pump lasts more than 1 years? (b) What is the probability that a pump lasts between 2 and 4 years? (c) Find the mean lifetime (d) Find the variance of the lifetime. (e) Find the cumulative distribution function of the lifetime. (f) Find the median lifetime....

  • can you please solve the problem 6 and not problem 5. thank you A new component...

    can you please solve the problem 6 and not problem 5. thank you A new component is placed in service and nine spares are available. The times to failure in days are independent exponential variables, Ti~ EXP(100). 10 What is the distribution of Ti? i- 1 What is the probability that successful operation can be maintained for at least 15 years? Hint: Use Theorem 8.3.3 to transform to a chi-square variable ow many spares would be needed to be 95%...

  • 4. The amount of time T (in hours) that a certain electrical component takes to fail...

    4. The amount of time T (in hours) that a certain electrical component takes to fail has an exponential distribution with parameter > 0. The component is found to be working at midnight on a certain day. Let N be the number of full days after this time before the component fails (so if the component fails before midnight the next day, N = 0). (a) What is the probability that the component lasts at least 24 hours? (b) Find...

  • Need only parts 5 and 6 Problem 6: 10 points Assume that X and Y are...

    Need only parts 5 and 6 Problem 6: 10 points Assume that X and Y are independent random variables uniformly distributed over the unit interval (0, 1) 1. Define Z = max (X, Y) as the larger of the two. Derive the CD. F. and density function for Z 2. Define W- min (X, Y) as the smaller of the two. Derive the C.D.F. and density function for W. 3. Derive the joint density of the pair (W, Z). Specify...

  • Xj are Random Variables which are continous and independent, means of Xj are 4 (E[ Xj...

    Xj are Random Variables which are continous and independent, means of Xj are 4 (E[ Xj ]=4), PDFs(Probability density function) of Xj are exponantial and they have the same PDFs (Probability density function). Let N is a RV(random variable) with Poisson PMF(probability mass function), whose mean is 7.(E[N]=7) Y = X1 + … + XN. If you find a function of Y which produces moment from table or by using a software like Matlab, Find PDF(Probability density function), Mean[E] and...

  • Problem 3 (Needed for Problem 4) A continuous random variable X is said to have an...

    Problem 3 (Needed for Problem 4) A continuous random variable X is said to have an exponential distribution, written Exp(X), if its probability density function f is such that le- if > 0 10 if x < 0 f(0) = 0 where > 0 is a real number. 1. Compute the mean of X 2. Compute the variance of X 3. Compute the cumulative distribution function F of X. Use this to show that for any real numbers s and...

  • You are given the following probability density function, 6x(r), for the cosine of the surface an...

    You are given the following probability density function, 6x(r), for the cosine of the surface angle, S, of a laser etching tool. The distribution function has one parameter, a, and one constant, c. -1sxs1 a) What is the value of the constant, e? b) What is the moment estimator for a? c) Explain how you can determine if this moment estimator is unbiased. t... . 24) denote a random sample of sample size n 24 with sample mean of-0.01 and...

ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT