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2008 4

# 2008 4 - Stat 230 Spring 2008 STAT 230 Spring 2008 Test 4...

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Stat 230 Spring 2008 STAT 230 - Spring 2008 - Test 4 SOLUTIONS Setup: Making lemonade requires lemons, sugar, and water. Good lemonade has a balance between sour (lemons) and sweet (sugar). If there are more lemons than sugar, it will be too sour, and if there is more sugar than lemons, it will be too sweet. Suppose you make 9 glasses of lemonade, where the distribution of the number of lemons, X, and the number of sugar cubes, Y, is given by the following joint probability function: x f ( x,y ) 0 1 2 0 0.05 0.05 0.05 y 1 0.05 0.25 0.05 2 0.1 0.05 0.35 1. [17 marks] Find the probability that: (a) [4 marks] A single glass of lemonade is i. actually just water P(water) = f (0 , 0) = 0 . 05 ii. too sweet P(sweet) = P ( X < Y ) = f (0 , 1) + f (0 , 2) + f (1 , 2) = 0 . 20 iii. too sour P(sour) = P ( X > Y ) = f (1 , 0) + f (2 , 0) + f (2 , 1) = 0 . 15 iv. good P(good) = f (1 , 1) + f (2 , 2) = 0 . 60 (b) [3 marks] 1 glass is water, 2 are too sweet, 2 are too sour, and 4 are good. Mult(9; 0.05, 0.20, 0.15, 0.60) f (1 , 2 , 2 , 4) = 9! 1!2!2!4! 0 . 05 1 0 . 20 2 0 . 15 2 0 . 60 4 = 0 . 022 (c) [3 marks] 4 are good and 2 are too sour.

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2008 4 - Stat 230 Spring 2008 STAT 230 Spring 2008 Test 4...

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