Solution Found!
The repair time (in hours) for a certain machine is a
Chapter 2, Problem 25E(choose chapter or problem)
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