quiz4-key

# quiz4-key - X E X =(0 f X(0(1 f X(1(2 f X(2 = 1 ← 4(2 pts...

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Quiz 4. September 29, 2010 Seat # _________ Name: ___ < KEY > ___ Closed book and notes. No calculators. Remember. You do not need to simplify answers. Consider flipping a coin twice, independently. For i = 1, 2, let H i denote that flip i results in "heads" facing up. Let X denote the number of flips that results in "heads" facing up. Then P( X = 0) = 1 / 4, P( X = 1) = 1 / 2, and P( X = 2) = 1 / 4. 1. (2 pts) Write f X , the probability mass function (pmf) of X . ___________________________________________________ f X ( x ) = P( X = x ) for every real number x . Therefore, f X (0) = 1 / 4, f X (1) = 1 / 2, f X (2) = 1 / 4, and f X ( x ) = 0 elsewhere. ___________________________________________________ 2. (2 pts) Write F X , the cumulative distribution function (cdf) of X . ___________________________________________________ F X ( x ) = P( X x ) for every real number x . Therefore, F X ( x ) = 0 for all x < 0, F X ( x ) = 1 / 4 for all 0 x < 1, F X ( x ) = 3 / 4 for all 1 x < 2, and F X ( x ) = 1 for all 2 x . ___________________________________________________ 3. (2 pts) Determine the value of E( X ), the expected value of
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Unformatted text preview: X . ___________________________________________________ E( X ) = (0) f X (0) + (1) f X (1) + (2) f X (2) = 1 ← ___________________________________________________ 4. (2 pts) Determine the value of E( X 2 ), the expected value of X 2 . ___________________________________________________ E( X 2 ) = (0 2 ) f X (0) + (1 2 ) f X (1) + (2 2) f X (2) = 3 / 2 ← ___________________________________________________ 5. (2 pts) Determine the value of P( X 2 = 4). ___________________________________________________ P( X 2 = 4) = P( X = 2) = 1 / 4 ← ___________________________________________________ ___________________________________________________ Ask yourself: Can you write the event X = 2 in terms of H 1 and H 2 ? Write on the back any concerns about the weekly quizzes or the course in general. IE 230 – Page 1 of 1 – Schmeiser...
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