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94年 - 94 淡江大學 轉學考 機率與統計學#56045
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1.請舉例說明何爲中央極限定理（central limit theorem)以及大數法則（law of large nuinljers).
其他申論題
(c) What is the power of this test? (4%)
#212653
(d) Suppose that the null hypothesis is H0:θ＞ 170 and the test statistic for this test is T, what is the p — value of tliis test ? if F = 175. (4%)
#212654
6 (a) What is meant by a multinomial experiment? (6%)
#212655
(b) Describe the Chi-Squared Goodness-of-fit Test. (8%)
#212656
2.有A,B，C,D,E共5個人，A君欲將一個紙條傳送給E君，A君在紙條上可能作的記號爲“+”或是“-”符號，而這個 紙條將透過A傳給B, B傳給C, C傳給D而最後D再傳給E,從過去經驗知道A君在紙條上作“+”的機率爲而 B, C, D三人接到紙條後可能會更改符號的機率皆爲現在E君發現手上的紙條符號是“十”，請問在此條件下A君當 初作的記號是“十”的機率爲多少？.
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3. Lei A, and Y be two iadependent, Possioa random variables with mean λ1 arid λ2. Find the conditional probability P(X = x | X+ Y = k), where x = 0,1, ..., k.
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4. Let X be a normal random variable with mean " and variance σ2. Compute the moment generating function E[etx] and then compute E(X3)
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(i) Show that and X1X2X3 has the same distribution where X1,X2 and X3 are i.i.d. U(0,1) r.v,s.
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【已刪除】(ii) Let Z be the number of , , where 0 ＜ t ＜ 1, show that Z lias a Poission distribution with parameter -log/.. (Hint: you can use the fact that which is the exponential dist. with mean 2)
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【已刪除】(i) Prove that
#212663
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