# Formula for expected value

The formula for the expected value is relatively easy to compute and involves several multiplications and additions. The expected value (or mean) of X, where X is a discrete random variable, is a To find E[ f(X) ], where f(X) is a function of X, use the following formula: E[ f(X) ]. Expected Value for a Discrete Random Variable. E(X)=\sum x_i p_i. x_i= value of the i th outcome p_i = probability of the i th outcome. According to this formula.

### Formula for expected value Video

The Expected Value and Variance of Discrete Random Variables If a random variable X is always less than or equal to another random variable Y , the expectation of X is less than or equal to that of Y:. The expected value is a key aspect of how one characterizes a probability distribution ; it is one type of location parameter. Example Going back to the first example used above for expectation involving the dice game, we would calculate the standard deviation for this discrete distribution by first calculating the variance: In probability theory , the expected value of a random variable , intuitively, is the long-run average value of repetitions of the experiment it represents. To empirically estimate the expected value of a random variable, one repeatedly measures observations of the variable and computes the arithmetic mean of the results. Work With Investopedia About Us Advertise With Us Write For Us Contact Us Careers. They only informed a small circle of mutual scientific friends in Paris about it. For example, suppose we toss a coin where the probability of heads is p. Expected Value for Multiple Events Of course, calculating expected value EV gets more complicated in real life. For other uses, see Expected value disambiguation. This is utilized in covariance matrices. Two thousand tickets are sold. Independent variables are a notable case of uncorrelated variables.

### Formula for expected value - unseren

Pascal, being a mathematician, was provoked and determined to solve the problem once and for all. You can calculate the EV of a continuous random variable using this formula: There are many applications for the expected value of a random variable. A More Complicated Expected Value Example The logic of EV can be used to find solutions to more complicated problems. This formula can also easily be adjusted for the continuous case. In probability theory , the expected value of a random variable , intuitively, is the long-run average value of repetitions of the experiment it represents. In particular, Huygens writes: If one considers the joint probability density function of X and Y , say j x , y , then the expectation of XY is. This formula makes an interesting appearance in the St. Welcome to STAT ! Definition, Word Problems T-Distribution Non Normal Distribution Chi Square Design of Experiments Multivariate Analysis Sampling in Statistics: