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final+fall+2011+solutions - ECI 114 Fall 2011 NAME Final...

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ECI 114 Fall 2011 NAME: _______________________ Final Examination ( Solutions ) Monday, December 5, 2011, 10:30 a.m. - 12:30 p.m. 100+5 bonus points Show your work . It’s not necessary to give a final numerical answer unless specifically asked, but you need to clearly provide all the information necessary to compute the final answer. Please circle or otherwise highlight your answer. Turn in your “crib sheet” and your normal etc. tables with your exam. GOOD LUCK! 1. (12 pts) For each of the following statements, circle the letter “T” if it is true, and “F” if it is false. T F a . ). ( ) ( ) ( C A B A C B A = T F b. You have tossed a fair die 6 times in a row and it landed showing a “3” every time. The probability of getting a “3” on the next toss is much much lower than 1/6. Due to independence, the probability is still 1/6 each time, independent of the past history. T F c. If A and B form a partition, then ] Pr[ ] Pr[ ] Pr[ 1 B A B A + = - . ] Pr[ B A = 0 since M.E; Pr[A]+Pr[B] = 1 since C.E T F d. The Central Limit Theorem shows that, if the sample size “n” is large enough, any sample mean is approximately normally distributed with mean and variance equal to their population values. T F e. |Cov(x, y)| ≤ σ x σ y Follows from ρ 2 = Cov(x, y) / σ x σ y and -1 ρ 2 1 T F f. For N elements taken n at a time, there are n! more combinations than permutations. n! more permutations than combinations - 1 -
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ECI 114 Fall 2011 2. 1. Geometric 2. Negative Binomial 3. Binomial 4. Hypergeometric 5. Poisson 6. Uniform 7. Exponential 8. Normal 9. t 10. Chi-squared 11. None of the above Place the number of the appropriate distribution in the blank next to each statement. Note that some statements may have more than one correct answer, but you need only give ONE answer. Some distributions may be used more than once and others not at all. (10*1.5 = 15 pts) 7 a. A distribution whose mean is equal to its standard deviation. 5 b. The arrival of events, where the interval between the arrivals is exponentially distributed. 10 c . The sum of squared independent normally-distributed random variables has this distribution. 4 d. Converges to the binomial distribution as the number of marbles in the urn, from which a finite number are sampled without replacement, goes to infinity. 3 e. Converges to the Poisson distribution as successes on discrete trials converge to arrivals in continuous time.
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