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Divide a line segment into two parts by selecting a point

Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman ISBN: 9780321923271 41

Solution for problem 13E Chapter 1.1

Probability and Statistical Inference | 9th Edition

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Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman

Probability and Statistical Inference | 9th Edition

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Problem 13E

PROBLEM 13E

Divide a line segment into two parts by selecting a point at random. Use your intuition to assign a probability to the event that the longer segment is at least two times longer than the shorter segment.

Step-by-Step Solution:
Step 1 of 3

 Answer:

 Step1 of 1:

         Consider the line as part of number line from 0 to 1, choosing a point same as choosing a line. So f(x) = 1.

          Let choose point ‘A’ corresponding to number ‘x’.

    The required cases is

     If x > 0.5 , = P({x: x > 2(1-x)})                                  

     If x < 0.5, =  P({x: (1-x) < 2 x})  

Then,

     =  P({x: x > and x < 1})

     =  P({x: x <  and x >0})

Here, p(required) =+   

                            =

 ...

Step 2 of 3

Chapter 1.1, Problem 13E is Solved
Step 3 of 3

Textbook: Probability and Statistical Inference
Edition: 9
Author: Robert V. Hogg, Elliot Tanis, Dale Zimmerman
ISBN: 9780321923271

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Divide a line segment into two parts by selecting a point

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