Concept explainers
(a)
Representation of random variable W .
(a)
Answer to Problem 43E
W represents the amount of time (in minutes) after the start of an hour at which a particular web server receives a randomly selected request.
Explanation of Solution
Given information:
Y : The amount of time (in seconds) after the start of an hour at which a randomly selected request is received by a particular web server.
Such that
We know that
Y represents the amount of time (in seconds)after the start of an hour at which a randomly selected request is received by a particular web server.
Such that
We also know that
There are 60 seconds in a minute.
Then
The time will become in minutes if we divide the time in seconds by 60.
Thus,
W represents the amount of time (in minutes)after the start of an hour at which a randomly selected request is received by a particular web server.
(b)
Probability distribution for random variable W .
(b)
Answer to Problem 43E
W has uniform density curve on the interval from 0 to 60 minutes.
Explanation of Solution
Given information:
Y : The amount of time (in seconds) after the start of an hour at which a randomly selected request is received by a particular web server.
Such that
For probability distribution,
Y has uniform density curve on the interval from 0 to 3600 seconds.
We know that
Y represents the amount of time (in seconds) after the start of an hour at which a randomly selected request is received by a particular web server.
Also,
Y has uniform density curve on the interval from 0 to 3600 seconds.
Since
Every data value in the distribution of Y is divided by the same constant 60.
Thus,
The shape of the distribution remains unchanged, if every data value is divided by the same constant.
Thereby,
The distribution of W has the same shape as the distribution of Y .
This implies
W has uniform density curve.
For uniform density curve,
0 seconds is same as 0 minutes.
In the same way,
3600 seconds is same as 60 minutes.
Thus,
W has uniform density curve on the interval from 0 to 60 minutes.
Chapter 6 Solutions
PRACTICE OF STATISTICS F/AP EXAM
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