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6.1 Overview: Combining Descriptive Methods and Probabilities Slide 1 In this chapter we will construct probability distributions by presenting possible outcomes along with the relative frequencies we expect. 6 5 Figure 4-1 6.2 Probability Distribution Slide 2 A random variable is a variable (typically represented by x) taking numerical values, determined by outcomes of an experiment associated with probabilities. A probability distribution is a graph, table, or formula that gives the probability for each value of the random variable. Example Slide 3 Roll a fair die and observe the number of dots on the face showing up. Let X= number of dots showing up = {1, 2, 3, 4, 5, 6} and each value is associated with a probability of 1/6 Then the Probability Distribution of X is: x 1 2 3 1 1 1 P(x) 6 6 6 4 5 6 1 1 1 6 6 6 Definitions Slide 4 A discrete random variable has either a finite number of values or countable number of values, where “countable” refers to the fact that there might be infinitely many values, but they result from a counting process. Example: X=the number of TV sets in a household A random variable is not discrete is called continuous random variable. It takes values associated with measurements on a continuous scale in such a way that there are no gaps or interruptions. Example: X=a newborn baby’s weight Graphs Slide 5 The probability Distribution is very similar to a relative frequency histogram, but the vertical scale shows probabilities. Figure 4-3 Requirements for Probability Distribution Σ P(x) = 1 Slide 6 where x assumes all possible values 0 ≤ P(x) ≤ 1 for every individual value of x Mean, Variance and Standard Deviation of a Probability Distribution Slide 7