265%20W08%20MT1 - IOE 265 W2008 Practice Exam I - Solutions...

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IOE 265 W2008 Practice Exam I - Solutions 1 of 7 Part I. Multiple Choice (10 questions, 3 points each, 30 points total) 1. Which of the following statements is (are) true about a Poisson probability distribution with parameter λ ? a. The mean of the distribution is λ b. The standard deviation of the distribution is λ c. The parameter λ must be between 0 and 1 d. All of the above 2. Which of the following is not a condition of a binomial experiment? a. There is a sequence of n identical trials. b. Each trial results in at least two outcomes. c. The trials are independent of each other. d. The probability of success p is constant from one trial to another. 3. If X is a continuous random variable defined on the interval [ A , B ], and the probability density function of X is (; , ) fxAB = 1/( ) 0 otherwise BA AxB ≤≤ then X is said to have: a. Geometric Distribution b. Uniform Distribution c. Hypergeometric Distribution d. Normal Distribution 4. Let k A A A K , , 2 1 be mutually exclusive and exhaustive events. Then for any other event B , () ()() ( ) ( ) k k A P A B P A P A B P B P + + = K 1 1 is known as: a. The multiplication rule b. Bayes Theorem c. The law of total probability d. The additive rule 5. Let 12 and A A be mutually exclusive and exhaustive events, with P 1 A = 0.10 and P 2 A = 0.25. Let B be any event such that P 1 (/ ) = 0.50 and P 2 = 0.80, then the P 1 (/) A B is: a. 0.05 b. 0.2* c. 0.25 d. None of the above *Using Bayes Theorem: ( ) () () 2 0 8 0 25 0 5 0 1 0 5 0 1 0 2 2 1 1 1 1 1 . ) . )( . ( ) . )( . ( ) . )( . ( A B P A P A B P A P A B P A P B A P = + = + =
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IOE 265 W2008 Practice Exam I - Solutions 2 of 7 6. If two events A and B are independent then: a. P(A)= P(A|B) b. P(A B)= P(A)×P(B) c. P(A)<=1 d. both (a) and (b) 7. The probability mass function of a discrete random variable X is defined as p(x) = x/10 for x = 0,1,2,3,4. The value of the cumulative distribution function F(x) at x= 3 is a. 0.10 b. 0.30 c. 0.60 d. 0.90 x0 1 2 34 f(x) 0 0.1 0.2 0.3 0.4 F(x) 0 0.1 0.3 0.6 1 8. Which of the following statements is not an example of a discrete random variable? a. The number of female respondents to a questionnaire about gender differences b. The number of defects per square meter of a cotton fabric c. The average sales a salesperson makes per year d. The number of school-age children with a single parent 9. Which of the following statements is always true?
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265%20W08%20MT1 - IOE 265 W2008 Practice Exam I - Solutions...

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