Let X have a Poisson distribution with parameter ?. Show that E( X ) = ? directly from the definition of expected value.[Hint: The first term in the sum equals 0, and then x can be canceled. Now factor out m and show that what is left sums to 1.]

Lecture 6: Random Variables 8.1 Random Variables - Definition: A random variable assigns a number to each outcome of a random circumstance, or, equivalently, a random variable assigns a number to each unit in a population. - Two broad classes of random variables: discrete random variables and continuous random variables. - Definitions: A discrete random variable can take one of a countable list of distinct values. Example: Number of years of studies. - A continuous random variable can take any value in an interval or collection of intervals. Example: Weight of a group of people Distribution of Random Variable