The men’s soccer team would, on the average, expect to play soccer 1.1 days per week. To find the expected value or long term average, μ, simply multiply each value of the random variable by its probability and add the products. In other words, after conducting many trials of an experiment, you would expect this average value. This “long-term average” is known as the mean or expected value of the experiment and is denoted by the Greek letter μ. When evaluating the long-term results of statistical experiments, we often want to know the “average” outcome. The Law of Large Numbers states that, as the number of trials in a probability experiment increases, the difference between the theoretical probability of an event and the relative frequency approaches zero (the theoretical probability and the relative frequency get closer and closer together). In his experiment, Pearson illustrated the Law of Large Numbers. To demonstrate this, Karl Pearson once tossed a fair coin 24,000 times! He recorded the results of each toss, obtaining heads 12,012 times. It gives information about what can be expected in the long term. Probability does not describe the short-term results of an experiment.
![what is term for probability weighted standard deviation what is term for probability weighted standard deviation](https://image.slidesharecdn.com/aprojectreportonoverviewofportfoliomanagementinindia-110420183443-phpapp02/95/a-project-report-on-overview-of-portfolio-management-in-india-50-728.jpg)
What is the probability that the result is heads? If you flip a coin two times, does probability tell you that these flips will result in one heads and one tail? You might toss a fair coin ten times and record nine heads. This means that over the long term of doing an experiment over and over, you would expect this average. The expected value is often referred to as the “long-term” average or mean. Classify discrete word problems by their distributions.Calculate and interpret expected values.