STAT-3090 Lecture Notes - Lecture 6: Random Variable, Sample Space, Probability Distribution
13 Feb 2018
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Chapter 6 - discrete probability distributions: information about the future. The ideas of randomness and uncertainty were introduced in the last chapter. This chapter extends those concepts by describing a pattern of randomness for an entire set of outcomes for a random phenomenon. Definition: random variables a variable that assumes numerical values associated with the random outcomes of an experiment, where one (and only one) numerical value is assigned to each sample point. Example 1: consider the sample space for tossing 3 coins. S = {hhh, hht, hth, thh, tth, tht, htt, ttt} Let"s redefine this situation to let x = the number of head observed in 3 tosses of a coin. Random variable takes on a countable number of outcomes (finite or infinite) Random variable takes on any points in one or more intervals (uncountable) We will study continuous random variables in chapter 7. Example 2: a box contains four slips of paper marked 1, 2, 3, and 4.
