100AHW4 - STAT 100A HWIV Solution Problem 1: Suppose we...

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Unformatted text preview: STAT 100A HWIV Solution Problem 1: Suppose we roll a biased die, the probability mass function is p (1) = . 1, p (2) = . 1, p (3) = . 1, p (4) = . 2, p (5) = . 2, and p (6) = . 3. Let X be the random number we get by rolling this die. (1) Calculate Var( X ). A: Var( X ) = 6 x =1 ( x- ) 2 p ( x ) = (1- 4 . 2) 2 . 1+(2- 4 . 2) 2 . 2+(3- 4 . 2) 2 . 1+(4- 4 . 2) 2 . 2 + (5- 4 . 2) 2 . 2 + (6- 4 . 2) 2 . 3 = 2 . 76. (2) Suppose the rewards (in the amount of dollars) for the six numbers are respectively h (1) =- 20, h (2) =- 10, h (3) = 0, h (4) = 10, h (5) = 20, and h (6) = 100. Please calculate Var[ h ( X )]. A: Var[ h ( X )] = 6 x =1 ( h ( x )- h ) 2 p ( x ) = (- 20- 33) 2 . 1 + (- 10- 33) 2 . 1 + (0- 33) 2 . 1 + (10- 33) 2 . 2 + (20- 33) 2 . 2 + (100- 33) 2 . 3 = 2061$ 2 . Problem 2: Suppose in the population of voters, the proportion of those who would vote for a certain candidate is 20%. If we randomly sample 100 people from the population of voters. Letcertain candidate is 20%....
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100AHW4 - STAT 100A HWIV Solution Problem 1: Suppose we...

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