Randomized Parameters in WebWork |

WeBWorK uses of the language perl with extra packages to author questions.

A parameter/variable in Perl starts with “$”, for example $a, $integer, $var.

Supported by the PGrandom package, in WeBWork random variables can be defined.

One random number

Generates a random number between the initial and final values in steps of increment.
```
random( $initial, $final, $increment )
```
If the increment is 0 or less, then random chooses a floating point number between $initial and $final using a small increment.$increment defaults to 1, if it is not supplied as an argument.

Example: $m=random(-2, 20, 3); generates a number among -2, 1, 4, …, 19 and stores it in the variable $m. Because the step is 3.
Generates a random number between 0 and $final.
```
rand( $final )
```
$final defaults to 1 if that argument is omitted.

Example: $r = rand(1); generates a number between 0 and 1 and store it in the variable $r.
Generate a nonzero random number between the initial and final values.
```
non_zero_random( $initial, $final );
```
Example: $coef = non_zero_random(2,7); generates a nonzero integer between 2 and 7 and stores it in the variable $coef.

Two or more different random numbers

Generate two or more different random numbers
```
do { $new = random($initial, $final); } until ( $new != $old );
```
$old is a predefined random number.

Example: do { $new = random(1, 6); } until ( $new != 3 ); generates a number between 1 and 6 but not equal to 3 and store it in the variable $new.
Generate a third different random number number
```
do { $third=random( $initial, $final ); } until (( $third != $first ) and ( $third != $second ));
```
$first and second are predefined random numbers.

Example: do { $third = random(1, 6); } until (($third != 3) and ($third != 5); generates a number between 1 and 6 but not equal to 3 and 5, and store it in the variable $third.

Random variables

To generate a random variable, we can use the RandomVariableName function supported by the package PCCmacros.pl.

Generate one random variable.
```
$var = RandomVariableName( type=>variable );
Context()->variables->are( $var=>'Real' );
```
In order to use the variable $var in formula, the second line is necessary.

Generate two different random variables

$vary = RandomVariableName(type=>variable);
do { $vary = RandomVariableName(type=>variable) } until ( $vary != $varx );
Context()->variables->add( $vary=>'Real' );

$varx is a predefined variable. Note that add() should be used for extra variables.

Example: The following codes will generate two different variables $varx and $vary.

$varx = RandomVariableName( type=>variable );
Context()->variables->are( $vars=>'Real' );
do { $vary = RandomVariableName(type=>variable )} until ( $vary != $varx );
Context()->variables->add( $vary=>'Real' );

A random element from a list

Randomizing from a list
```
list_random( $x1, $x2,...,$xn );
```
The element $xi can be a number, a letter or an expression.

Example: $Days = list_random(28, 29, 30, 31) randomly assigns a number from the list to the variable $Days.

Randomizing from an array

@array = ( $elem1, $elem2, ..., $elemn );
$arrayLength = scalar( @array );
$randIndex = random(0, $arrayLength);
$var = $array[ $randIndex ];

Example: Randomly assigns a number or the letter $x$ from the list to the variable $Days.

@array = ('x', 29, 30, 31);
$arrayLength = scalar( @array );
$randIndex = random(0, $arrayLength);
$Days = $array[ $randIndex ];

Randomized Parameters in WebWork

Fei Ye

2020/07/10

One random number

Two or more different random numbers

Random variables

A random element from a list

References