A probability distribution tells us the probability that a random variable takes on certain values.
For example, the following probability distribution tells us the probability that a certain soccer team scores a certain number of goals in a given game:
To find the expected value of a probability distribution, we can use the following formula:
μ = Σx * P(x)
where:
- x: Data value
- P(x): Probability of value
For example, the expected number of goals for the soccer team would be calculated as:
μ = 0*0.18 + 1*0.34 + 2*0.35 + 3*0.11 + 4*0.02 =  1.45 goals.
To calculate expected value of a probability distribution in R, we can use one of the following three methods:
#method 1 sum(vals*probs) #method 2 weighted.mean(vals, probs) #method 3 c(vals %*% probs)
All three methods will return the same result.
The following examples show how to use each of these methods in R.
Example 1: Expected Value Using sum()
The following code shows how to calculate the expected value of a probability distribution using the sum() function:
#define values
vals
#define probabilities
probs
#calculate expected value
sum(vals*probs)
[1] 1.45
Example 2: Expected Value Using weighted.mean()
The following code shows how to calculate the expected value of a probability distribution using the built-in weighted.mean() function in R:
#define values
vals
#define probabilities
probs
#calculate expected value
weighted.mean(vals, probs)
[1] 1.45 Example 3: Expected Value Using c()
The following code shows how to calculate the expected value of a probability distribution using the built-in c() function in R:
#define values
vals
#define probabilities
probs
#calculate expected value
c(vals %*% probs)
[1] 1.45 Notice that all three methods returned the same expected value.
Additional Resources
How to Calculate Mean in R
How to Calculate Geometric Mean in R
How to Calculate Weighted Mean in R