<sampleRandomNumbers/>

<sampleRandomNumbers/> is a Math component that generates random numbers from a specified range of values or within a normal distribution around a specified mean. It differs from the <selectRandomNumbers/> component in that the values can be altered within the document by resampling or changing one or more of the component’s attributes. The primary application of the <sampleRandomNumbers/> component is for use in simulations involving random numbers.

Attributes and Properties

Example: Default <sampleRandomNumbers/>

Without any attributes specified, the default sampling type is uniform, and the default interval is $[0, 1)$. In this example, there are two ways to view different samples: selecting another variant, or refreshing the page.

Example: Using a re-sampling button

Without any attributes specified, the default sampling type is uniform, and the default interval is $[0, 1)$. The <callAction> button can be used to resample the value.

Attribute Example: numSamples

<p>
  <sampleRandomNumbers numSamples="4" name="randomNumbers"/>
</p>
 
<callAction actionName="resample" target="$randomNumbers" >
  <label>Get New Numbers</label>
</callAction>
 
<p>The second number selected 
  <c>randomNumbers[2]</c> = $randomNumbers[2]
</p>

The <sampleRandomNumbers/> component is used with the numSamples attribute to select multiple random values in the default interval $[0,1)$. The default type is uniform.

Attribute Example: from, to

<p>
  <sampleRandomNumbers 
    name="x" 
    from="-5" 
    to="5" 
    numSamples="5" 
  />
</p>
 
<callAction actionName="resample" target="$x">
  <label>Get New Numbers</label>
</callAction>
 
<p>The second number selected 
  <c>x[2]</c> = $x[2]
</p>

The <sampleRandomNumbers/> component is used with the from and the to attributes to modify the default selection interval. The default type is uniform.

Attribute Example: type = “discreteUniform”

<p>
  <sampleRandomNumbers 
    name="x" 
    type="discreteUniform" 
    from="0" 
    to="10" 
    numSamples="5"
  />
</p>
 
<callAction actionName="resample" target="$x">
  <label>Get New Numbers</label>
</callAction>
 
<p>The second number selected 
  <c>x[2]</c> = $x[2]
</p>

The type attribute of the <sampleRandomNumbers/> component is specified as discreteUniform. The discreteUniform selection generates values from an evenly spaced range defined by the attributes to, from, and step. If left unspecified, the default step is 1.

Attribute Example: exclude

<setup>
<sampleRandomNumbers 
  name="n" 
  type="discreteUniform" 
  from="-4" to="4" 
  numSamples="3" 
  exclude="0"
/>
<number name="a" extend="$n[1]"/>
<number name="b" extend="$n[2]"/>
<number name="c" extend="$n[3]"/>
</setup>
 
<p>
  <math simplify="numberspreserveorder">
    $a x^2 + $b x + $c
  </math>
</p>
 
<callAction actionName="resample" target="$n">
  <label>New Coefficients</label>
</callAction>

The type attribute of the <sampleRandomNumbers/> component is specified as discreteUniform. Values can be excluded from the specified range used with this type using the exclude attribute.

Attribute Example: step

<p>
  <sampleRandomNumbers 
    name="x" 
    type="discreteUniform" 
    from="0" 
    to="20" 
    numSamples="5" 
    step="2"
  />
</p>
 
<callAction actionName="resample" target="$x">
  <label>Get New Numbers</label>
</callAction>
 
<p>The second number selected 
  <c>x[2]</c> = $x[2]
</p>

The type attribute of the <sampleRandomNumbers/> component is specified as discreteUniform. The discreteUniform selection generates values from an evenly spaced range defined by the attributes to, from, and step. If left unspecified, the default step is 1.

Attribute Example: type = “gaussian”

<p>
  <sampleRandomNumbers 
    name="x" 
    type="gaussian" 
    numSamples="10" 
    displayDigits="4"
  />
</p>
 
<callAction actionName="resample" target="$x">
  <label>Get New Numbers</label>
</callAction>
 
<p>The second number selected 
  <c>x[2]</c> = $x[2]
</p>

The type attribute of the <sampleRandomNumbers/> component is specified as gaussian. The gaussian selection generates standard normal variables (mean 0, variance 1). Alternatively, the mean as well as the variance or the standardDeviation attributes may be defined.

Attribute Example: gaussian with mean and variance

<p>With <attr>mean</attr> and <attr>variance</attr> attribute:
  <sampleRandomNumbers 
    name="x" 
    type="gaussian" 
    mean="10" 
    variance="2" 
    numSamples="10" 
    displayDigits="4"
  />
</p>
 
<callAction actionName="resample" target="$x">
  <label>Get New Numbers</label>
</callAction>
 
<p>The second number selected 
  <c>x[2]</c> = $x[2]
</p>

The type attribute of the <sampleRandomNumbers/> component is specified as gaussian. The gaussian selection generates standard normal variables (mean 0, variance 1). In this example, the mean and the variance are defined with attributes.

Attribute Example: gaussian with mean and standardDeviation

<p>With <attr>mean</attr> and <attr>standardDeviation</attr> attribute:
  <sampleRandomNumbers 
    name="x" 
    type="gaussian" 
    mean="10" 
    standardDeviation="2" 
    numSamples="10" 
    displayDigits="4"
  />
</p>
 
<callAction actionName="resample" target="$x">
  <label>Get New Numbers</label>
</callAction>
 
<p>The second number selected 
  <c>x[2]</c> = $x[2]
</p>

The type attribute of the <sampleRandomNumbers/> component is specified as gaussian. The gaussian selection generates standard normal variables (mean 0, variance 1). In this example, the mean and the standardDeviation are defined with attributes.