Enter the potential outcomes and their associated probabilities to calculate the expected value (mean) of a random variable. Ensure that the total probability sums to 1
Our expected value calculator helps to find the probability expected value of a discrete random variable (X) and give you accurate results.
In probability and statistics theory, the expected value is exactly what you might think it means intuitively: it is referred to as the return that you can expect for some kind of action, like how many multiple-choice questions you might get right if you guess on a multiple-choice test. The expected value of a random variable (X) denoted (E(X)) or (E[X]), uses probability to tell what outcomes to expect in the long run.
The formula for expected value (EV) is:
E(X) = mux = x1P(x1) + x2P(x2) + ... + xnPxn
E(X) = μx = Σⁿ(i=1) x𝑖 * P(x𝑖)
where;
The formula is discussed earlier; here we have an example for a better understanding of the concept.
Example:
If the numbers are (4,8,6,3) and the probability of each value is (0.1, 0.5, 0.04) and (0.36) respectively. Find the expected value ?
Solution:
Let's add the values into the expected value formula:
E(X) = 𝜇x = x1P(x1) + x2P(x2 + ... + xnP(xn)
Here,
X1 = 4 and P(x1) = 0.1
X2 = 8 and P(x2) = 0.5
X3 = 6 and P(x3) = 0.04
X4 = 3 and P(x4) = 0.36
So,
E(X) = (4)(0.1) + (8)(0.5) + (6)(0.04) + (3)(0.36)
E(X) = 0.4 + 4 + 0.24 + 1.08
E(X) = 5.72
From the authorized source of Wikipedia : Definition and formula
From the source of Investopedia : General understanding of EV
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