The repair time (in hours) for a certain machine is a

Chapter 2, Problem 25E

(choose chapter or problem)

Get Unlimited Answers
QUESTION:

The repair time (in hours) for a certain machine is a random variable with probability density function

\(f(x)=\left\{\begin{array}{cc}

x e^{-x} & x>0 \\

0 & x \leq 0

\end{array}\right.

\)

a. What is the probability that the repair time is less than 2 hours?

b. What is the probability that the repair time is between  and 3 hours?

c. Find the mean repair time.

d. Find the cumulative distribution function of the repair times.

Equation Transcription:

Text Transcription:

f(x)={_0         x{</=}0 ^xe-x     x>0

Questions & Answers

QUESTION:

The repair time (in hours) for a certain machine is a random variable with probability density function

\(f(x)=\left\{\begin{array}{cc}

x e^{-x} & x>0 \\

0 & x \leq 0

\end{array}\right.

\)

a. What is the probability that the repair time is less than 2 hours?

b. What is the probability that the repair time is between  and 3 hours?

c. Find the mean repair time.

d. Find the cumulative distribution function of the repair times.

Equation Transcription:

Text Transcription:

f(x)={_0         x{</=}0 ^xe-x     x>0

ANSWER:

Step 1 of 5:

Here it is given that the random variable under consideration is the repair time (in hours) of certain machine.

Let X be the random variable under consideration.

The probability density function of the random variable is given as

f(x)=x  for x>0

     =0 for x<0


Add to cart


Study Tools You Might Need

Not The Solution You Need? Search for Your Answer Here:

×

Login

Login or Sign up for access to all of our study tools and educational content!

Forgot password?
Register Now

×

Register

Sign up for access to all content on our site!

Or login if you already have an account

×

Reset password

If you have an active account we’ll send you an e-mail for password recovery

Or login if you have your password back