ass5 sol

ass5 sol - 08/09 THE UNIVERSITY OF HONG KONG DEPARTMENT OF...

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08/09 p. 1 THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT1301 Probability and Statistics I Assignment 5 Solution 1. Let 300 X be the mean of the 300 observations. Then by normal approximation, () ( ) ( ) 8888 . 0 22 . 1 2392 . 1 0787 . 0 0 300 0 0 300 = Φ = Φ < = < X P Y P 2. (a) 4168 . 0 5832 . 0 1 21 . 0 1 19 71 75 1 75 = = Φ = Φ = > X P (b) 0516 . 0 9484 . 0 1 63 . 1 1 60 19 71 75 1 75 = = Φ = Φ = > X P (c) Let c be the passing mark he should set. Then 642 . 46 282 . 1 19 71 9 . 0 19 71 1 9 . 0 = = = Φ = c c c c X P (d) If the normal assumption is violated, the calculations in (a) and (c) will be incorrect. However, the calculation in (b) is still valid because by central limit theorem, the sample mean of a random sample will follow a normal distribution approximately when the sample size is large. 3. Let be the outcome of i th roll, then are identically and independently distributed, with i X ,... , 2 1 X X 2 7 = i X E , 12 35 = i X Var . Therefore
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ass5 sol - 08/09 THE UNIVERSITY OF HONG KONG DEPARTMENT OF...

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