A continuous variable x is said to have a uniform distri-bution if the density function is given by-{+-+b=0f(x)a

Given that continuous variable if the density function is The time taken…

Answered: A continuous variable x is said to have…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Related questions

Question

A continuous variable x is said to have a uniform distri-
bution if the density function is given by
-{+-+
b
=
0
f(x)
a<x<b
otherwise
The corresponding density "curve" has constant
height over the interval from a to b. Suppose the time
(min) taken by a clerk to process a certain application
form has a uniform distribution with a = 4 and b = 6.
a. Draw the density curve, and verify that the total
area under the curve is indeed 1.
b. In the long run, what proportion of forms will take
between 4.5 min and 5.5 min to process? At least
4.5 min to process?
c. What value separates the slowest 50% of all pro-
cessing times from the fastest 50% (the median of
the distribution)?
d. What value separates the best 10% of all process-
ing times from the remaining 90%?

Expert Solution

Step 1: Determine the given variable

Given that continuous variable

$X tilde U open parentheses a comma b close parentheses$

if the density function is

$f left parenthesis x right parenthesis equals open curly brackets table row cell fraction numerator 1 over denominator b minus a end fraction space space space space space space space space space a less than x less than b end cell row cell space space space space 0 space space space space space space space space space space space space o t h e r w i s e end cell end table close$

The time taken by the clerk to process a certain application form has a uniform distribution with a=4 and b=6.