The expected value formula changes a little if you have a series of trials (for example, a series of coin tosses). When you have a series of trials. Your browser does not currently recognize any of the video formats available. Click here to visit our frequently. 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) ]. How to construct a probability distribution. Expected value formula for an arbitrary function. In this case, the values are headed towards 2, so that is your EV. Work With Investopedia About Us Advertise With Us Write For Us Contact Us Careers. Because the probabilities that we are working with here are computed using the population, they are symbolized using lower case Greek letters. Since it is measuring the mean, it should come as no surprise that this formula is derived from that of the mean. The equation is sometimes called the tower rule or the tower property ; it is treated under law of total expectation. But if you roll the die a second time, you must accept the value of the second roll. The basic expected value formula is the probability of an event multiplied by the amount of times the event happens: The expectation of X may be computed by. Your email address will not be published. Leave a Reply Cancel reply Your email address will not be published. Make a probability chart see: Follow Us Facebook Twitter Pinterest. Independent variables are a notable case of uncorrelated variables. Add the two values together: Multiply the gains X in the top row by the Probabilities P in the bottom row. The expected value is a key aspect of how one characterizes a probability distribution ; it is one type of location parameter. The American Mathematical Monthly. We will look at both the discrete and continuous settings and see the similarities and differences in the formulas. Expected Value in Statistics: The odds that you win the season pass are 1 out of For a three coin toss, you could get anywhere from 0 to 3 heads.