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How does your web browser get a file from the Internet? Your computer sends a request for the file to a web server, and the web server sends back a response. Let 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. The probability distribution of Ycan be modeled by a uniform density curve on the interval from 0to3600seconds. Define the random variable W=Y/60.

a. Explain what Wrepresents.

b. What probability distribution does Whave?

Short Answer

Expert verified

a. Wdenotes the amount of time (in minutes) that a randomly selected request is received by a given web server following the start of an hour.

b. Wexhibits a consistent density curve from data-custom-editor="chemistry" 0to60minutes

Step by step solution

01

Part(a) Step 1 : Given Information   

Given:

The probability distribution of Ycan be modeled by a uniform density curve on the interval from : 0to3600 seconds.

Random variable : W=Y/60.

02

Part(a) Step 2 : Simplification 

Y:The amount of time (in seconds) that a randomly selected request is received by a certain web server following the start of an hour.

So, W=Y60

We know that Yindicates the amount of time (in seconds) that a randomly selected request is received by a particular web server following the start of an hour.

We also know that a minute is divided into 60seconds.

If we divide the time in seconds by 60, we get the time in minutes.

As a result, Wdenotes the amount of time (in minutes) that a randomly selected request is received by a given web server following the start of an hour.

03

Part(b) Step 1 : Given Information   

Given :

The probability distribution of Ycan be modeled by a uniform density curve on the interval from : role="math" localid="1654002781486" 0to3600seconds.

Random variable : W=Y/60.

04

Part(b) Step 2 : Simplification 

Yhas a uniform density curve in the range of 0to3600seconds for probability distribution.

So, W=Y60

We know that Yindicates the amount of time (in seconds) that a randomly selected request is received by a particular web server following the start of an hour.

Yalso has a consistent density curve that spans the time range of data-custom-editor="chemistry" 0to3600seconds.

Because W=60, each data value in the Y distribution is split by the same constant.

If every data value is divided by the same constant, the form of the distribution remains intact.

As a result, the shape of W'sdistribution is the same as that of Y's.

This means that W's density curve is uniform

0seconds equals zero minutes for a homogeneous density curve.

3600secondsequals60minutes in the same way.

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