課程名稱︰機率 課程性質︰系定必修 課程教師︰陳文進 開課學院：電資學院 開課系所︰資工系 考試日期（年月日）︰98/4/9 考試時限（分鐘）：14:30~17:10 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : 1. (12%) Let A, B be two events where P(A) =0.4 and P(B) = 0.3, (a) If P(A∪B)=0.6, find P(A∩B), P(A|B) (b) If A and B are independent, find P(A∪B), P(A-B) 2. (10%) Let A, B, C be independent events, show that (a) A and B∩C are independent (b) A and B∪C are independent 3. (12%) In CSIE department, 4% of the men and 1% of the women are taller than 180cm. Futhermore, 60% of the students are women. (a) If a student is selected randomly, what's the probability that this student is taller than 180cm? (b) If the student selected is found to be taller than 180cm, what is the probability that the student is a woman? 4. (10%) A fair coin is tossed until either a head or five tails occurs. Let X be the random variable decribing the number of tosses of the coin Find E(X) and Var(X) 5. (12%) Let X and Y be two discrete random variables. (a) If P(X = k) = C/(4^k), k=1,2,3...,determine the constant C and find E(X) and Var(X) (b) If Y = (2X + 1)^2 , find E(Y) 6. (8%) Let X be the Poisson random variable with parameter λ. Find P(X is even). 7. (8%) If X is binomial random variable where E(X) = 6, and Var(X) = 2.4, find P(X =5). For the answer, you don't need to do the calculations such as 8^13 or 15!. 8. (16%) Suppose 2% of the items made by a factory are defective. (a) Find the probability P that there are 3 defective items in a sample of 100 items (b) Redo problem(a) using the Poisson approximation 9. (12%) The monthly world wide average number of airplane crashes of commercial airplane is 4. What is the probability that there will be (a) at least 2 crashes in the next month. (b) exactly 2 crashes in the next 3 months. --

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