Expected Value Definition:
An Expected Value is the weighted average of a random variable. Also called the mean.
Expected Value Notation
We represent the the expected value of a random variable X as E(X) or μxExpected Value Example
Take a fair coin where the probability of flipping a head is 1/2 and the probability of flipping a tail is 1/2.Expected Number of Heads in 2 coin flips = E(H)
E(H) = 2 flips * 1/2 probability of heads
E(H) = 1
Discrete Random Variable where P(x) is the probability mass function of X:
E(X) = Σxi · P(x)Continuous Random Variable
E(X) = -∞∫∞x · P(x)dxwhere x is the value of the continuous random variable X and P(x) is the probability density function
Expected Values of a constant times a random variable
When a is a constant and X and Y are random variables, we haveE(aX) = aE(x)
E(X + Y) = E(X) + E(Y)
Expected Value of a Constant:
Given a constant c, we haveE(c) = c
Expected Values of a product
When X and Y are independent random variables, we haveE(X · Y) = E(X) · E(Y)
Variance Definition Using Expected Value:
Variance of a random variable is the average value of the square distance from the mean value. In other words, how close the random variable is distributed near the mean value.σ2 = Var(X) = E(X - μ)2
Expected Values Calculator:
To see more on Expected Value, you can ask check out our Expected Value SearchHow does the Expected Value Calculator work?
Free Expected Value Calculator - This lesson walks you through what expected value is, expected value notation, the expected value of a discrete random variable, the expected value of a continuous random variable, and expected value properties.
What 7 formulas are used for the Expected Value Calculator?
E(aX) = aE(x)
E(X + Y) = E(X) + E(Y)
E(c) = c
When X and Y are independent random variables, we have E(X ยท Y) = E(X) · E(Y)
σ2 = Var(X) = E(X - μ)2
Discrete Random Variable: E(X) = Σxi · P(x)
Continuous Random Variable: E(X) = -∞∫∞x · P(x)dx
E(X + Y) = E(X) + E(Y)
E(c) = c
When X and Y are independent random variables, we have E(X ยท Y) = E(X) · E(Y)
σ2 = Var(X) = E(X - μ)2
Discrete Random Variable: E(X) = Σxi · P(x)
Continuous Random Variable: E(X) = -∞∫∞x · P(x)dx
What 6 concepts are covered in the Expected Value Calculator?
- constant
- a value that always assumes the same value independent of how its parameters are varied
- continuous random variable
- one which takes an infinite number of possible values
- discrete random variable
- a type of variable whose value depends upon the numerical outcomes of a certain random phenomenon
- expected value
- predicted value of a variable or event
E(X) = ΣxI · P(x) - product
- The answer when two or more values are multiplied together
- statistics
- Statistics is a discipline concerned with the analysis of data and decision making based upon data.
