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Multiple choice items(10 questions) (10 marks) 1. All the answers are true for the types of discrete probability distributions except a)binomial b)exponential c)poisson d)hypergeometric 2. If Ali does a single toss of a fair die, find the probability that the result in a number is less than 4 a) 1 4 b) 1 c) 3 1 d) 2 1 8 3. An urn contains four chips numbered 1 through 4.Two are drawn without replacement. Let the random variable X denote the larger of the two. Find E(X) a) 10 3 b) 12 c) 5 4 d) 9 3 8 4. Let the random variable X have the p.m.f as below.Find E (3𝑥 2 − 2𝑥 + 4) 𝑓(𝑥) = a) 8 9 b) 7 4 c) 6 5 ( |𝑥| + 1)2 , 𝑥 = −1,0,1 9 20 d) 3 5.All of the answers below are true for the types of continuous probability distribution except a) poisson b)uniform c)normal d)exponential 6.The cdf for a random variable Y is defined 𝐹𝑌 (𝑦) = 0 for y < 0 , 𝐹𝑌 (𝑦) = 4𝑦 2 − 3𝑦 4 for 0 ≤y<1 , 1 and 𝐹𝑌 (𝑦) = 1 for y>1 .Find P( 4 a) 10 17 b) 11 16 c) 17 19 d) 3 ≤𝑦≤ ) 4 12 13 7. Which one is not one of the properties of good point estimators? a) Unbiased b) Efficient(smaller variance) c)Consistency d) Sufficiency 8. A random sample of 100 survey shows students spends an average of 12 hours doing homework with standard deviation of 6.2 hours. How large a sample must be selected if we want to be 99% confident that the true mean is accurate within 1.5 hours? a) Less than 113 b) Less than 115 c) At least must be 113 d) At least must be 115 9. A manufacturer of car claims that a typical car gets 26 miles per galloon .A consumer group is skeptical of this claim and thinks that the mean gas mile age is less than 26miles per gallon .The group want to test the manufacturers claim using a random sample of 30 model cars. They will reject the claim if mean from the sample space is 𝑋̅ < 25.6 .What is probability that they are making a Type 1 error? a) 0.678 b) 0.594 c) 0.326 d) 0.925 10.Suppose that a random sample of size 5 is drawn from a uniform pdf 1 𝑓𝑦 (𝑦, 𝜃) = {𝜃 ,0 < 𝑦 < 𝜃 0, 𝑒𝑙𝑠𝑒𝑤ℎ𝑒𝑟𝑒 We wish to test 𝐻0 : 𝜃 = 2 versus 𝐻1 : 𝜃 > 2 By rejecting the null hypothesis if 𝑦𝑚𝑎𝑥 ≥ 𝑘. Find the value of k that makes the probability of commiting a Type 1 error equal to 0.05 a)2.76 b)1.29 c)3.63 d) 1.98