Expectation or expected value of an array - GeeksforGeeks

29 Apr, 2021
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++
Java
Python3
C#
PHP
Javascript
// CPP code to calculate expected// value of an array#include <bits/stdc++.h>using namespace std; // Function to calculate expectationfloat calc_Expectation(float a[], float n){    /*variable prb is for probability    of each element which is same for    each element  */    float prb = (1 / n);         // calculating expectation overall    float sum = 0;    for (int i = 0; i < n; i++)        sum += a[i] * prb;        // returning expectation as sum    return sum;} // Driver programint main(){    float expect, n = 6.0;    float a[6] = { 1.0, 2.0, 3.0,                 4.0, 5.0, 6.0 };         // Function for calculating expectation    expect = calc_Expectation(a, n);         // Display expectation of given array    cout << "Expectation of array E(X) is : "         << expect << "\n";    return 0;}
// Java code to calculate expected// value of an arrayimport java.io.*; class GFG{    // Function to calculate expectation    static float calc_Expectation(float a[], float n)    {        // Variable prb is for probability of each        // element which is same for each element        float prb = (1 / n);             // calculating expectation overall        float sum = 0;        for (int i = 0; i < n; i++)            sum += a[i] * prb;         // returning expectation as sum        return sum;    }     // Driver program    public static void main(String args[])    {        float expect, n = 6f;        float a[] = { 1f, 2f, 3f,                       4f, 5f, 6f };                 // Function for calculating expectation        expect = calc_Expectation(a, n);                 // Display expectation of given array        System.out.println("Expectation of array E(X) is : "                           + expect);    }} // This code is contributed by Anshika Goyal.
# python code to calculate expected# value of an array # Function to calculate expectationdef calc_Expectation(a, n):         # variable prb is for probability    # of each element which is same for    # each element    prb = 1 / n         # calculating expectation overall    sum = 0    for i in range(0, n):        sum += (a[i] * prb)             # returning expectation as sum    return float(sum)  # Driver programn = 6;a = [ 1.0, 2.0, 3.0,4.0, 5.0, 6.0 ] # Function for calculating expectationexpect = calc_Expectation(a, n) # Display expectation of given arrayprint( "Expectation of array E(X) is : ",                                 expect ) # This code is contributed by Sam007
// C# code to calculate expected// value of an arrayusing System; class GFG {         // Function to calculate expectation    static float calc_Expectation(float []a,                                    float n)    {                 // Variable prb is for probability        // of each element which is same        // for each element        float prb = (1 / n);             // calculating expectation overall        float sum = 0;                 for (int i = 0; i < n; i++)            sum += a[i] * prb;         // returning expectation as sum        return sum;    }     // Driver program    public static void Main()    {        float expect, n = 6f;        float []a = { 1f, 2f, 3f,                    4f, 5f, 6f };                 // Function for calculating        // expectation        expect = calc_Expectation(a, n);                 // Display expectation of given        // array        Console.WriteLine("Expectation"               + " of array E(X) is : "                             + expect);    }} // This code is contributed by vt_m.
<?php// PHP code to calculate expected// value of an array // Function to calculate expectationfunction calc_Expectation($a, $n){    /*variable prb is for probability    of each element which is same for    each element */    $prb = (1 / $n);         // calculating expectation overall    $sum = 0;    for ($i = 0; $i < $n; $i++)        $sum += $a[$i] * $prb;     // returning expectation as sum    return $sum;} // Driver Code$n = 6.0;$a = array(1.0, 2.0, 3.0,           4.0, 5.0, 6.0); // Function for calculating expectation$expect = calc_Expectation($a, $n); // Display expectation of given arrayecho "Expectation of array E(X) is : ".                        $expect . "\n"; // This code is contributed by Sam007?>
<script>// Javascript code to calculate expected// value of an array    // Function to calculate expectation    function calc_Expectation(a, n)    {        // Variable prb is for probability of each        // element which is same for each element        let prb = (1 / n);               // calculating expectation overall        let sum = 0;        for (let i = 0; i < n; i++)            sum += a[i] * prb;           // returning expectation as sum        return sum;    }  // driver function         let expect, n = 6;        let a = [ 1, 2, 3,                       4, 5, 6 ];                   // Function for calculating expectation        expect = calc_Expectation(a, n);                   // Display expectation of given array        document.write("Expectation of array E(X) is : "                           + expect); </script>
Output :  
Expectation of array E(X) is : 3.5
Time complexity of the program is O(n).As we can see that the expected value is actually average of numbers, we can also simply compute average of array.This article is contributed by Himanshu Ranjan. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above. 
vt_m
Sam007
sanjoy_62
Randomized
Writing code in comment?
Please use ide.geeksforgeeks.org,
generate link and share the link here.
Reservoir Sampling
Shuffle a deck of cards
Randomized Algorithms | Set 1 (Introduction and Analysis)
Karger's algorithm for Minimum Cut | Set 1 (Introduction and Implementation)
Random number generator in arbitrary probability distribution fashion
Randomized Algorithms | Set 2 (Classification and Applications)
Number guessing game in C
Generate 0 and 1 with 25% and 75% probability
Mid-Square hashing
Randomized Binary Search Algorithm