TAMU MATH 141  141_notes_Ch8 (12 pages)
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141_notes_Ch8
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 Texas A&M University
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 Math 141  Business Math I
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Chapter 8 Probability Distributions and Statistics Section 8 1 Distributions of Random Variables The value of the result of the probability experiment is a RANDOM VARIABLE If you roll a die we can let X be the number of dots showing If we have a hand of three cards X could be the number of clubs in the hand These examples are all finite discrete random variables Example Roll a single die and count the number of rolls until a 6 comes up outcome Y Finally the random variable can be continuous Example You are dealt a hand of 5 cards Find the probability distribution table for the number of hearts Graph this in a histogram 8 2 Expected Value The expected value for the variable X in a probability distribution is What is the MEAN of X E X X1 P X1 X 2 P X 2 X n P X n Example You are dealt a hand of 5 cards What is the expected number of hearts What was the X value that happened the most often What was the X value that was in the middle Example A sample of mini boxes of raisin bran cereal was selected and the number of raisins in each box was counted The results are shown in the table below of boxes 13 14 15 16 17 of raisins 10 14 19 16 12 Determine the appropriate random variable X and display the data in a probability histogram What is the expected value of X What is the RANGE of X values Histograms and Averages The MEAN expected value is where the histogram balances The MODE is the tallest rectangle The MEDIAN is where the area is cut in half The RANGE is the number of rectangles remember some may have a height of 0 Example Find the mean median and mode of the following test scores 77 46 98 87 84 62 71 80 66 59 79 89 52 94 77 72 85 90 64 70 Mean Median Mode Range Another way to measure spread QUARTILES 46 52 59 62 64 66 70 71 72 77 77 79 80 84 85 87 89 90 94 98 Q1 Q3 Box and whisker plot IQR Example A game consists of choosing two bills at random from a bag containing 7 one dollar bills and 3 ten dollar bills The player gets to keep the money picked How much should be
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