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無年度 - 主題課程_商學院統計：機率分配（離散型、連續型）#107837

科目：主題課程專用 | 選擇題數：4 | 申論題數：19

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選擇題 (4)

Y is distributed N(0,4), and X is distributed N(0,16). Please calculate B(Y2) and E(X3).(A) E(Y2) = 4 and E(X3) = 16(B) E(Y2) = 2 and E(X3) = 64(C) E(Y2) = 4 and E(X3) =0(D) E(Y2) = 2 and E(X3) = 8
(E) None of the above choices (a)-(d).
Suppose X and Y have a bivariate normal distribution with covariancc 1. X has a mean of 10 and standard deviation of 4.Y has a mean of 15 and standard deviation of 6. Z = 2X + 3Y. Which of the following statement is false?(A) The mean of Z is 65.(B) 'The variance of Z is 400.(C) The comeiation between X and Y is 1/24.(D) 2 follows a normal distribution.
(E) None of the above choices (a)-(d).
 3. X and Z are two independently distributed standard normal random variables. Y = X2+52. Please calculate E(Y). (A)-1.5 (B) 1 (C) 0.5 (D) 2.5
If X1. X2, .... are mutually independent norma! random variables, with their means all equal to 3 and variances equal to 10, what is the variance of ? (A) 400 (D) 200m  (B) 200 (C) 400m (E) None ofthe above choices (a)-(d).

申論題 (19)

The time elapsed, in minutes, between the placement of an order of pizza and its delivery is random with the

density function

627cb99acdee0.jpg#s-164,45

Suppose that it takes 15 minutes for the pizza shop to bake pizza once the shop receives the order. The mcan of

the time it takes for the delivery person to deliver pizza is _______.
A random variable X represents the number of defective mobile phone is a shipment of four iPhones to a local mobile phone stor(E) Assume that each mobile phone is equally likely to be defective or non-defective, and also assume that each mobile phone is defective or non-defective independently of the other mobile phones. Then the expected number of defective mobile phones is _______.
(a)  Find the probability that the oil will be sold out per week
(b)  Find the cumulative distribution function of Y
(c)  Find E(Y)
 Let X be the number of weeks before the prices change in a grocery store and p be the probability of updating the prices in a given week. The pricing decision is independent between any two weeks. If the distribution of X is described by
627cba52c29f8.jpg#s-188,39
where x =r, r+ 1,... The average duration of prices in this store is   (3)   if r =1.
(7)
(8)
針對以下各述,請回答「正確」或「不正確」,若回答「不正確」須進行更正·
 令X1,X2,...,627cbc945db52.jpg為來自N(μ,σ2)之随機樣本,様本平均數627cbcf02a6a2.jpg,樣本變異數S2= 627cbd12a842e.jpg,則627cbd237c45e.jpg之抽様分配為自由度n之1分配。

承上題,若様本數為16,樣本平均數627cbde32f8c2.jpg=100,樣本變異數S2=64,在信賴係數95%下t分配臨界值為2.131 ,可得母體平均數μ之95%信賴區間為(627cbe439edec.jpg)= (95.738,104.262),則吾人可宣稱信賴區間(95.738,104.262)包括母體平均數μ之機率為95% 。

令F(r1,r2)表自由度r1為以及r2之分配,627cbeb22a150.jpg表自由度為r1之卡方分配,當防r2趨近於無限大時,F(r1,r2)趨近於627cbef64d2ea.jpg。
f(x-1; μ)
f(x-1: μ)>f(x; μ) for x> μ

 A continuous random variable X has the exponential distribution with parameter 6>0 and it bas a pdf of the form 627cc2a11298c.jpg x>0 and zero otherwise. Please prove that P[X>a+t[X>a]-P[X>t]
 Customers enter a restaurant at random at a rate of four per minute. Assume that the number entering this restaurant in any given time interval has a Poisson distribution. The probability that at least two customers enter the restaurant in a given 0.25-minute interval is _______.
1.若想滿足至少80%的顧客需求,平均每天應進幾個定便當?
2.若每天只進8個定便當,則賣不完的機率為多少?
(15)
(16)