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102年 - 102 淡江大學 轉學考 機率與統計學#53094

科目：轉學考-機率與統計學 | 年份：102年 | 選擇題數：0 | 申論題數：10

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所屬科目：轉學考-機率與統計學

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申論題 (10)

(a) Calculate P(A\B).
(b) Are A and B independent events?
(a) Determine the joint and marginal probability distributions of U and V.
(b) Find out whether U and V are dependent or independent.
3. (15%) Suppose we choose arbitrarily a point from the square with corners at (2,1), (3,1), (2,2)， and (3,2). The random variable X is the area of the triangle with its corners at (2,1), (3,1), and the chosen point. Compute E[X],
(a) IF I = [a,β] (with a andβunknown, a ＜β. Find the maximum likelihood estimates (MLEs) for a and β.
(b) + 1]. Find the MLE for 6.
(a) Find the decision rule with the approximate size a of the test.
(b) Find the approximate power function of the test.
【已刪除】6. (15%) Suppose we have a dataset x1,...，xn that may be modeled as the realization of a random sample X1, • • •, Xn from an Exp distribution, where A is unknown. LetS n = X1+••• . + Xn. Construct a 90% confidence interval for A when n = 20. (The quantiles of the Gamrna(20,1) distribution are qo.o5 = 13.25 andqo.95 — 27.88. Denote the value of the sample mean by 亍20).