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Unformatted text preview: ) = F X ( b )-F X ( a ). (c) The PDF f X ( x ) is the derivative of the CDF. (d) Use the PDF: E ( X ) = R ∞-∞ x 3 f X ( x ) dx . 6. (a) c = 1 . 16. (b) For x ≥ 0, F X ( x ) = 1 . 16(1-e-x ). (c) P ( X > 1) = 1-P ( X ≤ 1). (d) E ( X ) = 0 . 686. 7. (a) For the CDF F X ( x ), need to consider 5 cases for x (b) Set F X ( x ) = 0 . 3 and solve for x . 8. (a) It’s a nice smooth increasing function. (b) CDFs are positive, increasing, approach 0 as x goes to-∞ , and approach 1 as x approaches ∞ . (c) Use the chain rule: d dx e-λx = λe-λx . (d) Set the CDF F X ( x ) = 1-e-λx equal to 0.5. Use the natural log function to solve for x . 1...
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This note was uploaded on 02/06/2012 for the course STAT 225 taught by Professor Martin during the Spring '08 term at Purdue University-West Lafayette.
- Spring '08