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題組內容

(6%) X is a binomial (5, 0.5) random variable.

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

其他申論題

沒有【段考】國小數學權限，請先開通．

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

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

(b) (3%) What is E[X|B]?

10%(a) Find the moment generating function of X.

10%(b) What is the distribution of X?

1. u / u / s / m / e / m ______________________________

2. t / o / s / p f / i / e / o / c / f ______________ ________________

3. o / c / k / o n / i / n / d / e / r ___________ __________________

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