ISYE2027hmwk1 - e-x/ 5 = 1 / 4. 10. Compute lim n ( 1-2 /n...

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ISyE 2027 Probability with Applications Fall 2011 R. D. Foley Homework 1 August 26, 2011 due on Monday, 29th August 1. Let the universal set Ω = { 1,2,. .., } . Let A denote the even integers in S , and B = { 1,. ..,7 } . What are (a) A c , (b) B c , (c) A B , (d) Ω B , and (e) B c A (where B c denotes the complement of B )? 2. Let the universal set Ω = [ 0,9.75 ) . Let A = [ 0,2 ) and B = ( 1.3,4 ] . What are (a) A c , (b) A B , (c) A B , and (d) A c B ? 3. Compute (a) n = 0 ( 1 / 4 ) n , and n = 0 4 n /n !. 4. Compute 4! and ( 11 9 ) where ± n k = n ! k ! ( n - k ) ! 5. (a) Show that n = 1 1 /n is finite, infinite, or undefined, whichever is ap- propriate. (b) Similarly, analyze n = 1 1 /n 2 . 6. Compute n = 0 1 n and n = 0 (- 1 ) n . 7. Compute R 2 0 8 x 7 dx , R 0 ( 1 / 9 ) e -( 1 / 9 ) x dx and R 0 ( 1 / 9 ) xe -( 1 / 9 ) x dx . 8. Compute R 2 x = 0 R x y = 0 6 xydydx and R x = 0 R y = 0 e -( 8 x + 9 y ) dydx . 9. Find the value of x such that
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Unformatted text preview: e-x/ 5 = 1 / 4. 10. Compute lim n ( 1-2 /n ) n . 11. In articles on-line at ajc.com related to cheating on the CRCT tests and in the press releases at the web site http://gaosa.org , nd at least three values for the probability of being 3 standard deviations or more above the mean. For each, give the value and the citation. Some good places to start looking are at APS Investigation Report Volume 1 and at 2009 CRCT Erasure Report 12. Prove or disprove: If f ( x ) > 0, then b R b f ( x ) dx 6 R b xf ( x ) dx for any b > 0....
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