quiz6-key - X 2 E X 2 = βˆ βˆ’βˆž ∞ y 2 f X y dy = ∠10...

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Quiz 6. October 13, 2010 Seat # _________ Name: _________________________ Closed book and notes. No calculator. Consider the probability density function f X ( y ) = 0.1 for 0 y c and zero elsewhere. 1. (2 pt) Show that c = 10. ____________________________________________________________ Set 1 = −∞ f X ( y ) dy = 0 c (0.1) dy = 0.1 c and solve for c . ____________________________________________________________ 2. (2 pt) Determine the value of f X (5.6). ____________________________________________________________ Because 0 5.6 c , immediately f X (5.6) = 0.1 ____________________________________________________________ 3. (2 pt) Determine the value of E( X ). ____________________________________________________________ E( X ) = −∞ y f X ( y ) dy = 0 10 y (0.1) dy = 5 ____________________________________________________________ 4. (2 pt) Determine the value of E(
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Unformatted text preview: X 2 ). ____________________________________________________________ E( X 2 ) = ∫ βˆ’βˆž ∞ y 2 f X ( y ) dy = ∫ 10 y 2 (0.1) dy = 33 1 / 3 ← ____________________________________________________________ 5. (2 pt) Determine the value of the cumulative distribution function F X (5.6). ____________________________________________________________ F X (5.6) = P( X ≀ 5.6) = ∫ βˆ’βˆž 5.6 f X ( y ) dy = ∫ 5.6 (0.1) dy = 0.56 ← ____________________________________________________________ ______________________________________________________________________ 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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