Chapter 7 Random Variables Random Variable A variable

Chapter 7 Random Variables

Random Variable � A variable whose value is a numerical outcome of a random phenomenon.

An example �You flip a coin 3 times and observe the number of tails. �Define the random variable X to be the number of tails.

�What are the possible values of X? 0 HHH 1 HHT HTH THH 2 HTT THT TTH 3 TTT

Discrete Random Variable This is a discrete random variable because the possible values of X are countable. A probability distribution is a table that shows the probability of each value occurring.

Probability Distribution �Let X = the number of tails observed when tossing a coin three times: The probability distribution is: X 0 1 2 3 P(X). 125. 375. 125

Probability Histogram �Shows the probability distribution in graphical form. P(X) X

Properties for a discrete R. V. 1) For every possible x value, 0 < P(x) < 1. 2) For all values of x, S P(x) = 1. sum

Let x be the number of courses for which a randomly selected student at a certain university is registered. X 1 2 3 P(X). 02. 03. 09 P(X = 4) =. 25 P(X < 4) =. 14 P(X < 4) =. 39 4 5 6 7 ? . 40. 16. 05

Finding the mean Let x be the number of courses for which a randomly selected student at a certain university is registered. X P(X) 1 2 3 4 5 6 7. 02. 03. 09. 25. 40. 16. 05 What would the mean (average) # of courses be?

To find the mean: Multiply each x value by its probability, and add them all up. 1(. 02) + 2(. 03) + 3(. 09) + 4(. 25) + 5(. 40) + 6(. 16) + 7(. 05) = 4. 66 (This is the average number of classes)

Find the mean Units Sold Probability 1000. 1 3000. 3 5000. 4 10, 000. 2 = 1000(. 1) + 3000(. 3) + 5000(. 4) + 10000(. 2) = 5000

The Variance: Find each value minus the mean. Square it. Multiply by the probability. Add them all up. Our previous example: (1000 – 5000)2(. 1) + (3000 – 5000)2(. 3) + (5000 – 5000)2(. 4) + (10000 – 5000)2(. 2) = 7, 800, 000

Standard Deviation is the square root of the variance. 2792. 8 =