Chapter 6.2, Problem 43E

(a)

To determine

Representation of random variable W .

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

  $W=\frac{Y}{60}$

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

  $W=\frac{Y}{60}$

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)

To determine

Probability distribution for random variable W .

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

  $W=\frac{Y}{60}$

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

  $W=\frac{Y}{60}$

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.