Expectation or expected value of an array
Expectation or expected value of any group of numbers in probability is the long-run average value of repetitions of the experiment it represents. For example, the expected value in rolling a six-sided die is 3.5, because the average of all the numbers that come up in an extremely large number of rolls is close to 3.5. Less roughly, the law of large numbers states that the arithmetic mean of the values almost surely converges to the expected value as the number of repetitions approaches infinity. The expected value is also known as the expectation, mathematical expectation, EV, or first moment.
Given an array, the task is to calculate the expected value of the array.
Examples :
Input: [1.0, 2.0, 3.0, 4.0, 5.0, 6.0]
Output: 3.5
Input: [1.0, 9.0, 6.0, 7.0, 8.0, 12.0]
Output: 7.16
Below is the implementation :
C++
#include <bits/stdc++.h>
using namespace std;
float calc_Expectation( float a[], float n)
{
float prb = (1 / n);
float sum = 0;
for ( int i = 0; i < n; i++)
sum += a[i] * prb;
return sum;
}
int main()
{
float expect, n = 6.0;
float a[6] = { 1.0, 2.0, 3.0,
4.0, 5.0, 6.0 };
expect = calc_Expectation(a, n);
cout << "Expectation of array E(X) is : "
<< expect << "\n" ;
return 0;
}
|
Java
import java.io.*;
class GFG
{
static float calc_Expectation( float a[], float n)
{
float prb = ( 1 / n);
float sum = 0 ;
for ( int i = 0 ; i < n; i++)
sum += a[i] * prb;
return sum;
}
public static void main(String args[])
{
float expect, n = 6f;
float a[] = { 1f, 2f, 3f,
4f, 5f, 6f };
expect = calc_Expectation(a, n);
System.out.println( "Expectation of array E(X) is : "
+ expect);
}
}
|
Python3
def calc_Expectation(a, n):
prb = 1 / n
sum = 0
for i in range ( 0 , n):
sum + = (a[i] * prb)
return float ( sum )
n = 6 ;
a = [ 1.0 , 2.0 , 3.0 , 4.0 , 5.0 , 6.0 ]
expect = calc_Expectation(a, n)
print ( "Expectation of array E(X) is : " ,
expect )
|
C#
using System;
class GFG {
static float calc_Expectation( float []a,
float n)
{
float prb = (1 / n);
float sum = 0;
for ( int i = 0; i < n; i++)
sum += a[i] * prb;
return sum;
}
public static void Main()
{
float expect, n = 6f;
float []a = { 1f, 2f, 3f,
4f, 5f, 6f };
expect = calc_Expectation(a, n);
Console.WriteLine( "Expectation"
+ " of array E(X) is : "
+ expect);
}
}
|
PHP
<?php
function calc_Expectation( $a , $n )
{
$prb = (1 / $n );
$sum = 0;
for ( $i = 0; $i < $n ; $i ++)
$sum += $a [ $i ] * $prb ;
return $sum ;
}
$n = 6.0;
$a = array (1.0, 2.0, 3.0,
4.0, 5.0, 6.0);
$expect = calc_Expectation( $a , $n );
echo "Expectation of array E(X) is : " .
$expect . "\n" ;
?>
|
Javascript
<script>
function calc_Expectation(a, n)
{
let prb = (1 / n);
let sum = 0;
for (let i = 0; i < n; i++)
sum += a[i] * prb;
return sum;
}
let expect, n = 6;
let a = [ 1, 2, 3,
4, 5, 6 ];
expect = calc_Expectation(a, n);
document.write( "Expectation of array E(X) is : "
+ expect);
</script>
|
Output
Expectation of array E(X) is : 3.5
Time complexity: O(n)
Auxiliary Space: O(1)
As we can see that the expected value is actually average of numbers, we can also simply compute average of array.
Last Updated :
13 Sep, 2022
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