To calculate the expected value in R, we use the formula for the expected value of a probability distribution. This value represents the average or mean of all possible outcomes, weighted by their probabilities.
Expected Value Formula
\mu = \sum (x \times P(x))
- x: sample value
- P(x): probability of the sample value
Example
Given:
X: 0.2, 0.3, 0.4, 0.5, 0.6
P(x): .1, .3, .5, .1, .2
\mu = (0.2 \times 0.1) + (0.3 \times 0.3) + (0.4 \times 0.5) + (0.5 \times 0.1) + (0.6 \times 0.2) = 0.48
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
x <- c(0.2, 0.3, 0.4, 0.5, 0.6)
probability <- c(0.1, 0.3, 0.5, 0.1, 0.2)
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: weights for the input data
- Returns: weighted mean of the values
Example: Calculate expected value
x <- c(0.2, 0.3, 0.4, 0.5, 0.6)
probability <- c(0.1, 0.3, 0.5, 0.1, 0.2)
weighted.mean(x, probability)
Output:
0.4
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
x <- c(0.2, 0.3, 0.4, 0.5, 0.6)
probability <- c(0.1, 0.3, 0.5, 0.1, 0.2)
c(x %*% probability)
Output:
0.48
Matrix multiplication returns the expected value 0.48.