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108年 - 108 彰化縣永光國小第二學期第三次成績評量試卷：數學#107971
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#462970
Problem 12. (2.5 %) Let Xi, 1 ≤ i ≤ 4 be independent Bernoulli random variable each with mean p = 0.1. Let X = That 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
#462972
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
#462973
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
#462974
(a) (3%) Find , where the condition B ={ X ≥μx}
#462975
(b) (3%) What is E[X|B]?
#462976
10%(a) Find the moment generating function of X.
#462977
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