1.1. Mathematical expectation, or expected value, of a random variable X which can take on values a1, a2, …, an, with probabilities p1, p2, …, pn, respectively is defined as E(X) = a1 p1 + a2 p2 + … + an pn

1.1.1. Expected Value does NOT need to be a member of the sample space

1.2. For binomial distribution, with a fixed amount of n trials, each with p probability of success, the expected value is np.

1.2.1. Expected Value does NOT need to be a member of the sample space

2. Related topics

2.1. Weighted Averages

2.1.1. Ex: A math class is graded on 3 tests, each 20% of the final grade, and a final exam which is 40% of the final grade. If a student averaged 89% on the first 3 tests, what score is needed on the final exam to average a 90% for the class?

2.2. Binomial Distributions

2.2.1. Ex: A family has 3 children. If the possible gender of each child is 50/50 M/F, what is the probability the family has 0,1,2, or 3 girls?