6.042J Lecture Notes - Lecture 11: Conditional Expectation, Random Variable, Sample Space

• School: MIT
• Department: Electrical Engineering and Computer Science
• Course: 6.042J
• Professor: Albert Meyer

Document Summary

The expectation or expected value of a random variable is a single number that reveals a lot about the behavior of the variable. The expectation of a random variable is also known as its mean or average. More precisely, the expectation of a random variable is its average value when each value is weighted according to its probability. Expected value of a random variable: if r is a random variable de ned on a sample space s, the the expectation of r is. In general, if r is a random variable with a uniform distribution on {a , a , , a }, then the expectation of r is simply the average of the a "s: Note: the random variable might never actually take on the expected value. The expected value of an indicator random variable. The expected value of an indicator random variable for an event is just the probability of that event.