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December 08, 2011 Warm Ups 13-4 5 2 3 1. In expansion of (3x - 2y) , find x y term 2. In expansion of (2x3 + 1/x )12, find the constant term. December 08, 2011 Let X be the sum when you roll 2 die. Make a frequency table for X x 2 3 4 5 6 7 8 9 10 11 12 P(X=x) Find (with grapher) median: mode: mean: variance: Population standard deviation: Sample Standard deviation December 08, 2011 The mean is also called the "expected value" E(X) mean = Example: Find k, and then find the mode, median, and mean values of X in the probability distribution function below. Do this with and without a grapher. x P(X=x) mode: median: mean: 1 1/10 2 2/10 3 4/10 4 k December 08, 2011 The book gives all sorts of fancy formulas and shortcuts for finding variance, but since we aren't going to be on this topic for a long time, let's just keep it simple and use our formula and our graphers to find variance. x -2 P(X=x) Find (with grapher) E(X): standard deviation: variance: We could even find E(2X): Var(X+3): Sd(1/X): -1 0 1 2 December 08, 2011 How many tails would you expect when a coin is tossed 5 times? Make a probability distribution table and calculate E(X) to back this up. Would you ever roll this many tails? x P(X=x) 0 1 2 3 4 5 December 08, 2011 A dart board consisting of concentric circles of radius 1,2,and 3 units is placed on a wall. Upon throwing a dart, which lands on some random location on the wall, a player will receive $8 is the smaller circle is hit, $6 if the middle annular region is hit, and $4 if the outer annular region is hit. However, should the player miss the dart board altogether they would lose $7. The probability that the player misses the dart board and hits the wall is .5 a. How will the player fare in this game? ( i.e. what is the E(X)) 8 b. Is it a fair game? x P(X=x) 8 6 4 -7 6 4 December 08, 2011 #13-4 p. 541 1-7 skip 3 December 08, 2011