Below are the steps to calculate the expected value with the help of our expectation calculator:
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An Expected Value Calculator is an online tool that helps to calculate the expected value of a random variable using various potential outcomes and their corresponding probabilities.
The expected value is often denoted as 𝐸(𝑋). It represents the average outcome of a random variable when an experiment is repeated many times. Essentially, the expected value is the long-run average value of repetitions of the experiment it represents.
To calculate the expected value, multiply each possible outcome by its probability and then sum up all these products. The formula for the expected value is:
E(X) = μx = x1P(x1) + x2P(x2) + ... + xn P(xn)
E(X) represents the expected value of the random variable X.
μx denotes the mean of X.
∑ stands for the summation symbol.
P(xi) indicates the probability of the outcome xi.
xi is the ith possible outcome of the random variable X.
n is the total number of possible outcomes.
I represents a possible outcome of the random variable X.
This section will demonstrate how to calculate expectation value by solving examples.
Example:
Calculate the expected value for the following probability distribution using the expected value formula.
X: 0, 1, 2, 3, 4
P(X): 0.10, 0.25, 0.30, 0.20, 0.15
Solution:
By using the expected value formula:
x | P(x) | x × P(x) |
0.00 | 0.10 | 0.00 |
1.00 | 0.25 | 0.25 |
2.00 | 0.30 | 0.60 |
3.00 | 0.20 | 0.60 |
4.00 | 0.15 | 0.60 |
∑xi = 10.00 | ∑ P(xi) = 1.00 | ∑xi × P(xi) = 2.05 |
Example:
In a game, you flip a coin. If it lands on heads, you win $3, if it lands on tails, you lose $2. What is the expected value of this game?
Solution:
To find the expected value (EV), we use the formula:
EV=∑ (Outcome ×Probability)
Outcomes and Probabilities:
Heads: Win $3 (Outcome = +3) $, Probability =0.5= 0.5=0.5
Tails: Lose $2 (Outcome = -2) $, Probability =0.5= 0.5=0.5
Calculation:
EV = (3×0.5) + (−2×0.5)
EV = 1.5+(−1)
EV = 0.5
The expected value of this game is $0.50. This means, on average, you can expect to gain $0.50 per coin flip over the long run.
1. How do you find the expected value in a chi-square?
In a chi-square test, you can calculate the expected value for a cell by using the formula:
Expected Value = (Row Total * Column Total) / Grand Total
If you're not already well-versed in the chi-square test, check out our Chi-square calculator first.
2. How to Calculate the Expected Value?
To find the expected value, you just need to follow these steps:
3. Can the expected value be negative?
Yes. The expectation value of an operator can be positive, negative, or even complex. The variance will be positive definite. But the expectation value can be any number.