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MATH 110 Chapter 8 & 9 Test Outline EXPECTED VALUE (8.5) Super easy ones (when the PDF is already given to you as a table and all you need to do is multiply down the columns and add across) Example: Find the expected value of the random variable X. X 2 4 6 7 P(X) 0.3 0.2 0.1 0.4 EXPECTED VALUE (8.5) Still easy but the probabilities are given graphically Example: Find the expected value of the random variable X. EXPECTED VALUE (8.5) Still easy but the probabilities are given in a ‘word problem’. Example: A wedding photographer has a big event that will yield a profit of $2000 with a probability of 0.8 or a loss (due to unforeseen circumstances) of $500 with a probability of 0.2. What is the photographer’s expected profit? EXPECTED VALUE (8.5) Lotteries, Raffles, etc. (Practice makes perfect. Please do a lot of these. I posted lots of problems like these…including some YouTube videos.) Example: Suppose you buy 1 ticket for $2 in a lottery with 1000 tickets. The prize for the one winning ticket is $300. What are your expected winnings? EXPECTED VALUE (8.5) Lotteries, Raffles, etc. Example: Find the expected payback for a game in which you bet $4 on any number from 0 to 199 if you get $400 if your number comes up. EXPECTED VALUE (8.5) Lotteries, Raffles, etc. Example: In roulette, there are 18 red compartments, 18 black compartments & 2 compartments that are not red or black. If you bet $2 on red and the ball lands on red, you get to keep the $2 you paid to play and you win another $2. Otherwise, you lose your $2 bet. What is your expected payback if you bet $2 on red? BASIC STATISTICS (9.1 & 9.2) Easy…mode, median, mean, range and standard deviation Example: For the following set of numbers, find the mode, the median, the mean (round to nearest tenth), the range and the standard deviation (round to the nearest hundredth): 41 60 56 35 40 36 BASIC STATISTICS (9.1 & 9.2) Mean and standard deviation from a Frequency table Example: Find the mean (round to the nearest tenth) and standard deviation (round to the nearest hundredth) of the placement scores in the table below. Value 4 7 8 3 Frequency 3 2 1 4 BASIC STATISTICS (9.1 & 9.2) Grouped means and standard deviations Example: Find the mean (round to the nearest tenth) and standard deviation (round to the nearest hundredth) of the data below: Interval 1-4 5-8 9-12 13-16 Frequency 3 2 1 4 BASIC STATISTICS (9.1 & 9.2) Chebyshev’s Theorem Example: Find the fraction of all the numbers of a data set that must lie within 3 standard deviations from the mean. BASIC STATISTICS (9.1 & 9.2) Chebyshev’s Theorem Example: In a certain distribution, the mean is 50 with a standard deviation of 6. Use Chebyshev’s Theorem to find the probability that a number lies between 26 and 74. Write your final answer rounded to the nearest thousandth.