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無年度 - 主題課程_理工學院機率論：機率分配（離散型、連續型）#107979

科目：主題課程專用 | 選擇題數：0 | 申論題數：7

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Problem 12. (2.5 %) Let Xi, 1 ≤ i ≤ 4 be independent Bernoulli random variable each with mean p = 0.1. Let X = 6286eaec587b8.jpgThat is, X is a Binomial random variable with parameters n = 4 and p = 0.1. Then, (i) E[X1|X=2]=0.1
(ii) E[X1| X=2]=0.5
(iii) EXi|X=2]=0.25
Problem 11. (2.5 %) To obtain a driving license, John needs to pass his driving test. Every time John takes a driving test, with probability 1/2, he will clear the test independent of his past. John failed his first test. Given this, let Y be the additional number of tests John takes before obtaining a license. Then, 
(i) E[Y] =1
 (ii) E[Y] =2
 (iii) E[Y]=0
Problem 13. (2.5 %) Let X1, X2, X3 be independent random variables with the continuous distribution over [0,1]. Then P(X1＜X2＜X3) = 
(i) 1/6 
(ii) 1/3 
(iii) 1/2
 (iv) 1/4

(a) (3%) Find 6286ec35d7a9f.jpg, where the condition B ={ X ≥μx}

(b) (3%) What is E[X|B]?
10%(a) Find the moment generating function of X.
10%(b) What is the distribution of X?