Test1_makeup_sols - AMS310.03 TEST 1-A FORM Fall 2003 1...

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AMS310.03 TEST 1--A FORM Fall 2003 1. PRINT YOUR NAME HERE______________________________ USE ONLY UPPER CASE LETTERS. UNDERLINE YOUR LAST NAME TWICE. 2. STUDENT ID NUMBER 3. CHECK TO MAKE SURE THAT YOUR TEST HAS 7 PAGES INCLUDING THIS ONE. 4. SHOW YOUR WORK FOR ALL QUESTIONS IN SECTIONS II. NO CREDIT WILL BE GIVEN FOR A NUMERICAL ANSWER WITHOUT AN ARGUMENT. POINTS POINTS OFF POINTS EARNED SECTION I 30 QUESTION II-1 20 QUESTION II-2 20 QUESTION II-3 20 QUESTION II-4 10 ----------------------------------------------------------------------------------------------- TOTAL 100 - __________ = ___________(SCORE) 1
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AMS310 TEST 1 Form A PAGE 2 OF 7 PRINT YOUR NAME HERE ___________________________ Part I: Short answer questions. Very few calculations are required. Write the correct answer in the space provided by the question number. _______1. If there are 12 items in a box, how many samples of n=2 can we choose without replacement? Ans)) 12 2 12! 66 2!10! C = = _______2. P(A) = 0.2 , P(B) = 0.5, P(A B )= 0.05. P(A B) =____. Ans)) ( ) ( ) ( ) ( ) P A B P A P B P A B = + - = 0.2+0.5-0.05 = 0.65 ________3. Suppose we toss a single die and the result is the number of dots observed. Then S={1,2,3,4,5,6}. Let A= {2,4,6}, and let B={3 ,4,5,6}. Then A B = __________. Ans)) {1,2} B = so, {1,2,4,6} A B = _______4. P(A)=0.5 P(B)= 0.6, P(A B) = 0.35 P(B|A)= Ans)) ( ) ( | ) ( ) P B A P B A P A P = 0.35 0.7 0.5 = = _______5. Given S= {1,2,3,4,5,6} the outcomes of the toss of 1 die. Let A={4,5,6} and let B={1,2,5}. Which statement below is correct? (a) A and B independent events. A and B are not mutually exclusive events. (b) A and B are dependent events. A and B are not mutually exclusive event. (c) A and B are independent. A and B are mutually exclusive. (d) A and B are dependent events. A and B are mutually exclusive. Ans)) (B) i) {5} A B = therefore, A and B are not mutually exclusive. ii) 1 ( ) 2 P A = , 1 ( ) 2 P B = and 1 ( ) ({5}) 6 P A B P = = then, 1 1 1 1 ( ) ( ) ( ) 2 2 4 6 P A P B P A B = = = Therfore, A and B are dependent events _______6. P(A|B) =0.1 P(A)=0.2 P(B)=0.6 P(A B)= ______ Ans)) ( ) ( | ) ( ) 0.1 0.6 0.06 P A B P A B P B = = = 2
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AMS310 TEST 1 form A PAGE 3 OF 7 PRINT YOUR NAME HERE______________________ WRITE CORRECT ANSWER IN THE SPACE PROVIDED BY THE QUESTION NUMBER ________ 7. Given the values for F(x), the cumulative distribution function of X for values of X for which f(x)>0. Find P(X 1.0). x 0 0.5 1.0 1.5 2.0 3.0 F(x) 0.1 0.4 0.5 0.6 0.8 1.0 Ans)) ( 1.0) 1 ( 1.0) 1 ( 0.5) 1 0.4 0.6 P X P X P X = - < = - = - = ________8. Evaluate 5 0 2 ! 5 ) 5 ( - = - e x x x x Ans)) 2 5 0 5 ( 5) ! x x x e x P - = - 2 ( ) ! x all x e x λ λ μ - = - : Variation formula of Poisson distribution with 5 λ = then 5 μ λ = = = 2 5 σ λ = = __________ 9. X has Poisson distribution with λ =2. Use Table 2 to find Pr({X >3}). Ans)) ({ 3}) 1 ({ 3}) 1 0.857 0.143 P X P X = - = - = ___________ 10. Given the values of X and f(x) below . Find the value of μ , the mean of X. X -3 -2 0 4 f(x) 0.2 0.2 0.2 0.4 Ans)) by definition of μ , ( ) ( 3) (0.2) ( 2) (0.2) 0 (0.2) 4 (0.4) all x f x μ = = - + - + + ° 0.6 0.4 0 1.6 0.6 = - - + + = 3
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AMS310 TEST 1- PAGE 4 OF 7 PRINT YOUR NAME HERE______________________ LONGER QUESTIONS. FOR THESE QUESTIONS WHEREVER THERE IS A NUMERICAL ANSWER YOU NEED TO SHOW HOW YOU ARRIVED AT IT. YOUR SCORE WILL BE DETERMINED BY YOUR PRESENTATION OF YOUR METHOD.
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  • Fall '03
  • Mendell
  • Normal Distribution, Probability theory, 1 inch, 1 2 k, 0.25 inch, 0.05 inches

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