we provide an informal definition of expected value and we discuss its computation in this lecture, while we relegate a more rigorous definition to the (optional) lecture entitledExpected value and the Lebesgue integral.
For the example of rolling two dice and summing the results, there is an easier way to calculate the expected value. This random variable can be viewed as the sum of two random variables: the first die roll and the second die roll: Zsum of two die=Xfirst die+Ysecond dieHow...
be two random variables and let and be two constants. Then, The next example shows an important application of the linearity of the Lebesgue integral. The example also shows how the Lebesgue integral can, in certain situations, be much simpler to use than the Stieltjes integral when computing ...
Consider the difference of two random variables: one binomial(10,000, 0.5) and the other binomial(5,000, 0.5). The probability that the mixed strategy does better is the probability that the difference of these two is less than 2,450. Approximate both as independent normally distributed variab...
Therefore, if the probability of an event happening is p and the number of trials is n, the expected value will be n*p.Discrete Variables A random variable is the possible outcome(s) of a random probabilistic event. There are two types of random variables; continuous and discrete....
DEFINING EXPECTED VALUE The expected value concept uses two main mathematical concepts—random variables and probabilities. To understand a random variable, let us assume that an experiment results in a certain number of outcomes and each of the outcomes is assigned a numerical value. A random ...
The similarity degree between the expectation of two random intervals is studied by means of a hypothesis testing procedure. For this purpose, a similarity measure for intervals is introduced based on the so-called Jaccard index for convex sets. The measure ranges from 0 (if both intervals are ...
ex·pect·ed value (ĭk-spĕk′tĭd) n. 1.A quantity expressing a typical or average value of a random variable. 2.The sum (for discrete variables) or integral (for continuous variables) of the product of a random variable with its probability density function, over its range of val...
Formula for Expected Value The formula for expected value is: EV=∑P(Xi)×XiEV=∑P(Xi)×Xi where: X is a random variable Xi are specific values of X P(Xi) is the probability of Xi occurring Thus, the EV of arandom variableX is taken as each value of the random variab...
RANDOM variablesSTATISTICSTESTINGHYPOTHESISp values are extensively reported in practical hypothesis testing situations. Although carefully studied by Dempster and Schatzoff, the stochastic aspect of p values is often neglected. In this expository note we borrow from Dempster and Schatzoff to rekindle ...