How to Calculate Expected Value in R?

In this article, we are going to see how to calculate the excepted value using R Programming Language. A probability distribution describes all the possible values of random variables in the given range.

Expected value of a probability distribution:

Where X is a Sample value and P(x) is a Probability of a simple value

Example:

X: 0.2, 0.3, 0.4, 0.5, 0.6

P(x): .1, .3, .5, .1, .2

μ = (0.2*0.1) + (0.3*0.3) + (0.4 * 0.5) + (0.5*0.1) + (0.6*0.2) = 0.48

Explanation: The expected value of probability distribution calculated with Σx * P(x) formula

Method 1: Using sum() method

sum() method is used to calculate the sum of given vector

Syntax: sum(x)

Parameters:

x: Numeric Vector

Example: Calculate expected value

R

# create vector for value
x <- c(0.2, 0.3, 0.4, 0.5, 0.6)

# create vector for probability
probability <- c(.1, .3, .5, .1, .2)

sum(x*probability)

Output:

0.48

Method 2: Using weighted.mean() method

It is used to get the weighted arithmetic mean of input vector values.

Syntax: weighted.mean(x, weights)

Parameters:

• x: data input vector
• weights: It is weight of input data.
• Returns: weighted mean of given values

Example: Calculate expected value

R

x <- c(0.2, 0.3, 0.4, 0.5, 0.6)

probability <- c(.1, .3, .5, .1, .2)

# calculate expected value
weighted.mean(x, probability)

Output:

0.48

Method 3: Using c() method

It is used to combine the arguments passed to it. And %*% operator is used to multiply a matrix with its transpose

Syntax: c(…)

Parameters:

…: arguments to be combined

Example: Calculate expected value

R

x <- c(0.2, 0.3, 0.4, 0.5, 0.6)

probability <- c(.1, .3, .5, .1, .2)

# calculate expected value
c(x %*% probability)

Output:

0.48