MAT 135A Final: MAT 135A Final Exam Fall 2018
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Do not turn this page until told to. Each of the 4 problems is worth 30 points. Justify every step. (c) a die is rolled twice. Let z equal the sum of the outcomes, and let w equal the rst outcome minus the second. Use the stirling approximation to simplify your answer: assume that raindrops are spherical, and let d be the diameter of a random raindrop. According to the marshall palmer model, the distribution of d is exponential with parameter . Recall that a ball of diameter d has volume (a) prove that e(d) = 1. 6 d3 and surface area d2. (b) we collected 1000 random raindrops, and their total volume is 3150 mm3. We conclude that the average volume of a raindrop is 3. 15 mm3. Expectation px (k) = (cid:0)n k(cid:1)pk(1 p)n k. , n np px (k) = (1 p)k 1p. 1, 2, 3, . px (k) = e k/k!