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Unformatted text preview: { 1 , 2 , 3 , 4 , 5 , 6 } . (a) Determine Pr( X < 4). (b) Determine Pr( X 4). (c) Determine Pr(6 < X < 10). 13. Suppose X is a random variable having PMF f ( x ) = x 21 , x = 1 , 2 , 3 , 4 , 5 , 6 . (a) Determine E ( X ). (b) Determine E ( X 2 ). (c) Determine E { ( X3) 2 } . 1 14. Suppose X is a Ber( p ) random variable. (a) Show that E ( X k ) = p for all positive integers k . (b) Determine E { ( Xp ) 2 } . (c) Determine E { ( Xp ) 3 } . 15. Determine the set of real numbers such that f ( x ) = , x = x 1 2 , x = x 2 1 2 , x = x 3 is a PMF on the sample space { x 1 ,x 2 ,x 3 } . 2...
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 Spring '11
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