Chapter 6.2, Problem 44E

(a)

To determine

Representation of random variable V .

Answer to Problem 44E

V represents the amount of time (in seconds).

Explanation of Solution

Given information:

X : The amount of time (in minutes) that Sally has to wait for the bus on a randomly selected day.

Such that

  $V=60X$

We know that

X represents the amount of time (in minutes) that Sally has to wait for the bus on a randomly selected day.

Such that

  $V=60X$

We also know that

There are 60 seconds in a minute.

Then

The time will become in seconds if we multiply the time in minutes by 60.

Thus,

V represents the amount of time (in seconds) that Sally has to wait for the bus on a randomly selected day.

(b)

To determine

Probability distribution for random variable V .

Answer to Problem 44E

V has uniform density curve on the interval from 0 seconds to 480 seconds.

Explanation of Solution

Given information:

X : The amount of time (in minutes) that Sally has to wait for the bus on a randomly selected day.

Such that

  $V=60X$

For probability distribution,

X has uniform density curve on the interval from 0 to 8 minutes.

We know that

X represents the amount of time (in minutes) that Sally has to wait for the bus on a randomly selected day.

Also,

X has uniform density curve on the interval from 0 to 8 minutes.

Since

  $V=60X$

Every data value in the distribution of X is multiplied by the same constant 60.

Thus,

The shape of the distribution remains unchanged, if every data value is multiplied by the same constant.

X has uniform density curve.

In the same way,

V also has a uniform density curve.

For uniform density curve,

0 minutes is same as 0 seconds.

In the same way,

8 minutes is same as 480 seconds.

Thus,

V has uniform density curve on the interval from 0 seconds to 480 seconds.