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Unformatted text preview: ECI 114 Fall 2011 Name Solutions_______ Midterm 2 (100 points) Monday, November 14, 2011 Show your work. It’s not necessary to give a final numerical answer unless specifically asked, but you need to provide all the information necessary to compute the final answer. Please circle or otherwise highlight your answer. Turn in your “crib sheet” and normal table with your exam. GOOD LUCK! 1. For each of the following statements, circle the letter “T” if it is true, and “F” if it is false. (3 pts * 8 = 24 pts) T F a. The geometric distribution is a special case of the binomial distribution where r = 1. The geometric dist. is a special case of the negative binomial distribution where r =1 T F b. Both binomial and negative binomial distributions assume Bernoulli trials. In addition, the geometric distribution also assumes Bernoulli trials T F c. For any continuous random variable Y, ∫ ∞ = . 1 ) ( dy y f ∫ ∞ ∞ = . 1 ) ( dy y f T F d. If a random variable Y is distributed exp(λ), then E(Y) = λ. E [Y] = 1/ λ T F e. For any continuous random variable Y, Pr[a ≤ Y < b] = Pr[a < Y ≤ b]. Since Pr[Y=a] = Pr[Y=b] = 0 for a CRV. T F f. For a continuous random variable, the median is the point at which there is a 5050 chance of falling above it or below it (this sentence is true; now you indicate whether the next sentence is true or false). Therefore, for any continuous distribution, the mean and median are the same. True if the distribution is symmetric. T F g. The exponential and chisquared distributions are both special cases of the gamma family of distributions. T F h. If X and Y are independent random variables, then Var(X  Y) = Var(X + Y). Both = Var(X) + Var(Y). It may not be intuitive, but if X and Y are independent, they 1 vary independently, the spread of the distribution of Y is the same as the spread of Y, and the spreads of the two distributions add....
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 Fall '08
 Mocktarian
 Probability theory, Discrete probability distribution

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