STAT 400 Lecture AL1 Spring 2015 Dalpiaz Homework 1 due Friday January 30 by 3 00 p m Please include your name with your last name underlined your NetID and your discussion section number at the top of the first page Do NOT use a computer You may only use and 1 4 on a calculator Show all work 1 Evaluate the following integrals a 2 x e 3 x dx b 0 c 1 2 2 x sin x dx x dx 1 x 4 cos x 2 1 2 2 sin x 2 x dx 2 0 2 0 1 2 u 1 du u4 2 1 u3 du 2 1 u4 du 0 x 1 x 4 dx 1 c x 2 e 3 x dx x 2 e 3 x 2 x e 3 x 3 e 3 x 3 3 3 b x sin x dx 0 0 a 2 0 2 27 1 1 1 1 12 8 24 2 Let c 0 Consider f x y x c y and A x y 0 y x 1 a Sketch A That is sketch x y 0 y x 1 b Set up the double integral s of f x y over A with the outside integral w r t x and the inside integral w r t y 1 x x c y dy dx 0 0 c Set up the double integral s of f x y over A with the outside integral w r t y and the inside integral w r t x 1 1 x c y dx dy 0 y d Find the value of c such that f x y dx dy 1 A 1 x 1 1 c 1 c c 2 x c y dy dx 1 x dx 1 1 2 3 6 3 2 0 0 0 c 4 3 Consider f x y x y 3 and A x y 0 y 1 y x 2 a Sketch A That is sketch x y 0 y 1 y x 2 b Set up the double integral s of f x y over A with the outside integral w r t x and the inside integral w r t y 2 x 3 x y dy dx 0 0 1 1 c 1 x y 3 dy dx 0 Set up the double integral s of f x y over A with the outside integral w r t y and the inside integral w r t x 2 3 x y dx dy 0 y 1 d Use either b or c to evaluate f x y dx dy A 2 1 1 1 2 3 x 2 3 1 5 3 x y dx dy 2 x y x y dy 2 y 2 y dy 0 0 0 y 1 5 1 1 1 6 y 1 1 y4 y 0 y 2 12 12 12 2 OR 2 x 3 x y dy dx 0 0 1 1 1 2 1 x5 x x y 3 dy dx dx dx 4 4 0 1 0 5 1 1 1 12 24 2 8 4 Evaluate the following sums do NOT use a calculator a k 3 2 5k 0 6 b 2 k 1 c k 1 2k k 5 k a 2 2 2 2 2 3 4 5 6 k 5 5 5 5 5 k 3 Geometric series Base 2 2 first term k 1 base k 3 5 b 0 6 2 k 1 5 3 1 1 5 1 5 2 125 4 5 1 0 02 50 0 6 3 0 6 5 0 6 7 0 6 9 k 1 Base 0 6 2 0 36 Geometric series 0 6 2 k 1 k 1 c 2k 0 6 3 0 216 first term 1 0 36 0 64 1 base 2k 2 0 21 2 2 2 3 2 4 k 0 k 0 1 2 3 4 k 5 k 27 0 3375 80 e 2 1 2 2 4 2 3 3 e 2 7 5 Suppose P A 0 70 a Find P A B b P A B 0 80 P B 0 50 Find P A B Find P A B c P A 0 70 P B 0 50 P A B P B 0 30 1 P B 0 50 0 80 0 10 0 40 0 20 a P A B 0 30 b P A B 0 90 c P A B 0 30 0 60 0 50 6 Suppose P A 0 40 P B 0 34 P C 0 55 P A B 0 19 P A C 0 25 P B C 0 17 P A B C 0 07 a Find P A B C P A B C 0 75 b Find P A B C P A B C 0 67 c Find P A B C P A B C 0 37 7 Let a 1 Suppose S 2 3 4 5 6 and P k a Find the value of Must have c c k 2 3 4 5 6 k a that makes this is a valid probability distribution P x 1 all x b c c c c k 2 a k c a a 1 a2 a3 c a4 c a5 first term 1 base a2 1 1 a Find P outcome is odd P outcome is odd P 3 P 5 P 7 P 9 a a 1 a a 1 a a 1 a a 1 a3 first term 1 base a5 a 1 a2 1 a7 1 a 1 a 2 1 a9 1 a 1 a2 OR P outcome is odd P 3 P 5 P 7 P 9 a a 1 a a 1 a a 1 a a 1 a3 a5 a7 a9 c 1 a a 1 P outcome is even P 2 P 4 P 6 P 8 a a 1 a a 1 a a 1 a a 1 a2 a4 a6 a8 a P outcome is odd P outcome is odd P outcome is even 1 c P outcome is odd a P outcome is odd 1 P outcome is odd 1 a 1 Find P outcome is less than or equal to 5 P outcome is less than or equal to 5 P 2 P 3 P 4 P 5 a a 1 a a 1 a a 1 a a 1 a2 a3 a4 a 1 a 3 a 2 a 1 a 4 a5 a 4 1 a 4 1 1 a 4 OR P outcome is less than or equal to 5 1 P 6 P 7 P 8 P 9 a a 1 a a 1 a a 1 a a 1 1 a 6 a7 a8 a9 a 1 1 5 first term 1 a 1 1 base 1 a 1 1 a 4 8 Suppose S 2 3 4 5 6 and a Find the value of Must have c P k c P x …
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