Homework Help: math

Posted by raksha on Sunday, October 28, 2007 at 12:38am.

Suppose that the time (in hours) required to repair a machine is an exponentially distributed random variable with parameter λ (lambda) = 0.5.

What's the probability that a repair takes less than 5 hours? AND what's the conditional probability that a repair takes at least 11 hours, given that it takes more than 8 hours?

math - drwls, Sunday, October 28, 2007 at 1:21am
The probability distribution you are talking about is
f (x; lambda) = lambda exp^-(lambda x), x > 0

It is discussed at http://en.wikipedia.org/wiki/Exponential_distribution

The probability that a repair takes less than x is
F (x; lambda) = 1 - exp(-lambda x)
For x = 1 - exp(-2.5) = 0.918

The fraction taking 8 hours or more to repair is
exp(-4) = 0.01832
The fraction taking 11 hours to repair is
exp(-5.5) = 0.00409
That means that 409/1832 = 22% of the repairs taking 8 hours or more require more than 11 hours.

Answer this Question

Related Questions

Statistics - Hi folks, I'm having trouble with figuring out the intensity ...
MATH - A company makes three products X, Y and Z. Each product requires ...
MATH- please help! - A company makes three products X, Y and Z. Each product ...
MATH-PLEASE HELPPP!!!! - A company makes three products X, Y and Z. Each product...
math- im really confused! please help!! - A company makes three products X, Y ...
intro to probability - For the sheet-metal stamping machine in a certain factory...
Differential Equations - Model radioactive decay using the notation t = time (...
Operation Management - Customers arrive at service window every 3.6 minutes(...
statistics - ten randomly selected people were asked how long they slept at ...
Statistics - Suppose X is a normally distributed random variable with the mean u...

For Further Reading

First Name:
School Subject:
Answer: