HW-01

# HW-01 - HOMEWORK FOR EXST 7036 (Chapter 1) Student Name:...

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HOMEWORK FOR EXST 7036 (Chapter 1) Student Name: Tanza Erlambang 1.3) Each of 100 multiple-choice questions on an exam has four possible answers but one correct response. For each question, a student randomly select one response as the answer a. Specify the distribution of the student’s number of correct answers on the exam Answer : Binomial distribution N = 100, π = ¼ = 0.25 b. Based on the mean and standard deviation of that distribution, would it be surprising if the student made at least 50 correct response?. Explain your reasoning Answer : Mean = µ = n π = 100 (0.25) = 25 Standard deviation = σ = √ n π (1- π ) = √ 100 x 0.25 (1- 0.25) = 4.33 Yes, surprisingly, since 50 correct responds are greater than mean (25) Then, the standard deviation of 50 correct responds is greater than standard deviation of mean (25) too. 1.6) Genotype AA, Aa and aa occur with probability ( π 1 , π 2 , π 3 ). For n = 3 independent observations, the observed frequencies are (n1, n2, n3). a. Explain how you can determine n3 from knowing n1 and n2. Thus, the multinomial distribution of (n1, n2, n3) is actually two-dimensional Answer: since, n = 3, thus n3 = 3 – n1 – n2 1

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b. Show the set of all possible observations (n1, n2, n3) with n = 3 Answer : all possible observations are : (3, 0, 0), (2, 1, 0), (2, 0, 1), (1, 2, 0), (1, 1, 1), (1, 0, 2), (0, 3, 0), (0, 2, 1), (0, 1, 2), (0, 0, 3) c. Suppose ( π 1 , π 2 , π 3 ) = (0.25, 0.50, 0.25). Find the multinomial probability that (n1, n2, n3) = (1, 2, 0) Answer: Multinomial probability is : P (n1, n2, n3) = (n!/n1!n2!n3!) π 1 n1 π 2 n2 π 3 n3 =(3!/1!2!0!) (0.25) 1 (0.50) 2 (0.50) 0 = 3 (0.25) (0.25) = 0.1875 d. Refer to ( c ) what probability distribution does n1 alone have?. Specify the values of the sample size index and parameter for that distribution. Answer: Binomial for n = 3 trials, and parameter π = 0.25 1.7) In his autobiography “A sort of Life”, British author Graham Greene described a period of severe mental depression during which he played Russian Roulette. This “game” consists of putting a bullet in one of the six chambers of a
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## This note was uploaded on 04/11/2010 for the course EXST 7036 taught by Professor Brianmarx during the Spring '10 term at LSU.

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HW-01 - HOMEWORK FOR EXST 7036 (Chapter 1) Student Name:...

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