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Unformatted text preview: E(X). 1 http://www.stat.ucla.edu/~dinov/courses_students.dir/08/Spring/STAT35.dir f. What are the expected value, E(X), and the standard deviation, SD(X), if k = 2 and θ =4? Validate your closed‐form mathematical expression by using the Pareto Distribution Modeler. E(X) = 8, SD(X) = ∞ Problem 3 a. What is the probability that the diameter of a randomly selected tree will be at least 10 in.? Will exceed 10 in.? 0.3341 b. What is the probability that the diameter of a randomly selected tree will exceed 20 in.? 0.000032 2 http://www.stat.ucla.edu/~dinov/courses_students.dir/08/Spring/STAT35.dir c. What is the probability that the diameter of a randomly selected tree will be between 5 and 10 in.? 0.5785 d. What value c is such that the interval (8.8−c, 8.8+c) includes 98% of all diameter values? 6.5138 3 http://www.stat.ucla.edu/~dinov/courses_students.dir/08/Spring/STAT35.dir Problem 4 a. If a specimen is acceptable only if its hardness is between 67 and 75, what is the chance that a randomly chosen specimen has an acceptable hardness? 0.7936 b. If the acceptable range of hardness is (70−c, 70+c), for what value of c would 95% of all specimens have acceptable hardness? 5.8799 c. If the acceptable range is as in part (a) and the hardness of each of ten randomly selected specimens is independently determined, what is the expected number of acceptable specimens among the ten? 7.94 4...
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This note was uploaded on 01/22/2014 for the course STATISTICS 35 taught by Professor Dinov during the Spring '09 term at UCLA.

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