Expected Value
by Eric Thuemmel
1. Definitions
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?
3. Applications
3.1. Games of chance
3.1.1. Gambling
3.1.1.1. Roulette
3.1.1.2. Blackjack
3.1.1.3. Poker
3.1.2. Family Games
3.1.2.1. Yahtzee
3.1.2.2. Pig
3.2. Insurance
3.2.1. Risk Analysis
3.3. Medical Field
3.3.1. Drug Testing