×
Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 4 - Problem 23se
Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 4 - Problem 23se

×

# A distribution that has been used to model tolerance ISBN: 9780073401331 38

## Solution for problem 23SE Chapter 4

Statistics for Engineers and Scientists | 4th Edition

• Textbook Solutions
• 2901 Step-by-step solutions solved by professors and subject experts
• Get 24/7 help from StudySoup virtual teaching assistants Statistics for Engineers and Scientists | 4th Edition

4 5 1 255 Reviews
27
4
Problem 23SE

A distribution that has been used to model tolerance levels in bioassays is the logistic distribution with parameters α and β. The cumulative distribution function of the logistic distribution is The parameter α may be any real number; the parameter β may be any positive number. Let X be a random variable with this distribution.

a. Find the probability density function fx(x).

b. Show that fx(x) is symmetric around α, that is, fx(α -x) = fx(α+ x) for all x.

c. Explain why the symmetry described in part (b) shows that μx = α. You may assume that μx exists.

Step-by-Step Solution:

Step 1 of 3:

(a)

In this question, we are asked to find the probability density function for given cumulative distribution function of logistic distribution. Where may be any real number; the parameter may be any positive number..

Let be a random variable with this distribution.

We know the formula for calculating the cumulative distribution function (CDF) is: Then probability density function can be found as a =  = =  ) assume t = ]

=     ] (using chain rule of differentiation)

=  [  ]

=  [ ]

= ……………(1)

Hence probability distribution function = Step 2 of 3

Step 3 of 3

##### ISBN: 9780073401331

Unlock Textbook Solution