# Computing expected value

The expected value (or mean) of X, where X is a discrete random variable, is a weighted average of For the above experiment (with the die), calculate E(X 2). the formula for computing its expected value is a straightforward implementation of the informal definition given above: the expected value of X is the weighted. The formula for the expected value is relatively easy to compute and involves several multiplications and additions. In the above proof, the treatment of summation depends on absolute convergence , which assumes existence of E X. I am having a hard time understanding where the information goes. Over many many draws, the theoretical value to expect is 6. Multiply 1 by 2 to get: If the possible outcomes of the game or the bet and their associated probabilities are described by a random variable, then these questions can be answered by computing its expected value, which is equal to a weighted average of the outcomes where each outcome is weighted by its probability. Eberly College of Science. If one considers the joint probability density function of X and Y , say j x , y , then the expectation of XY is. Theory of probability distributions. The intuition however remains the same: The use of the letter E to denote expected value goes back to W. Thanks to all authors for creating a page that has been read , times. We will look at both the discrete and continuous settings and see the similarities and differences in the formulas. X n having a joint density f: Let be an absolutely continuous random variable.

### Computing expected value - auf die

When is a discrete random variable having support and probability mass function , the formula for computing its expected value is a straightforward implementation of the informal definition given above: How do I calculate the mean of a group of numbers? Not all random variables have a finite expected value, since the integral may not converge absolutely; furthermore, for some it is not defined at all e. They only informed a small circle of mutual scientific friends in Paris about it. I also like that it shows the possibility of winning multiple prizes. The odds that you win the season pass are 1 out of Privacy policy About Wikipedia Disclaimers Contact Wikipedia Developers Cookie statement Mobile view. However, there is an easier computational formula. Add the numbers together, and divide the sum by the number of numbers. Suppose random variable X can take value x 1 with probability p 1 , value x 2 with probability p 2 , and so on, up to value x k with probability p k. If the possible outcomes of the game or the bet and their associated probabilities are described by a random variable, then these questions can be answered by computing its expected value, which is equal to a weighted average of the outcomes where each outcome is weighted by its probability. Neither Pascal nor Huygens used the term "expectation" in its modern sense.