→ jenny200638:感謝大大 我再將書讀熟一次!! 01/23 23:52
※ 引述《jenny200638 (J大)》之銘言：
: 這是98交大生資的題目
: 想要對答案但是同學都沒有這個領域的
: 所以就希望有人可以一起練習看看囉!!
: 只有四題是機率，我題目複製上來好了!!
: http://ppt.cc/jW@P 覺得PDF比較好讀的可以點連結!
: 其實在寫的時候也覺得不難，但是本身能力不好所以想謹慎一點><
: 1. A box contains 3 red and 5 blue balls.
: (a) Balls are drawn at random without replacement until a red ball is drawn.
: What is the probability that exactly 3 drawn are required.
: (b) Balls are drawn at random with replacement until a red ball is drawn.
: What is the probability that exactly 3 drawn are required.
: (c) Balls are drawn at random with replacement 6 times. What is the
: probability that 3 red balls and 3 blue balls are drawn in these 6 times.
: 2. Let X, Y be independently uniformly distributed over (0, 1).
: Define Z = X^2, and W = max(X,Y).
: (a) Find distribution function of Z.
: (b) Find E(Z).
: (c) Find distribution function of W.
: (d) Find E(W).
: 3. Let the joint density function of random variables X and Y be given by
: f (x,y) = { 2 if 0≦y≦x≦1
: 0 o.w
: (a) Calculate the marginal density function of X.
: (b) Calculate P(2X+2Y < 3).
: 4. Let XI, X2, . . ., Xn be a random sample of size n from a continuous
: distribution
: function F with meanp and variance 02. Let the sample mean
: (a) What are E(X) and Var ( X)
: (b) Let u =loo, 變異數=40, n=90. Use central limit theorem to approximate
: P( 99 < X < 101 ). (Express your solution by using the standard normal
: distribution function )
: 我算出的答案依序:
: 1.(a) 5/28
: (b) 75/256
: (c) 0.01287
: 2.(a) f(z)=1/2z^(-1/2) , 0<=z<=1
: (b) 1/3
: (c) 知道是順序統計量，但算到一半就卡= =
: (d) 同上
: 3.(a) 2x ,0<=x<=1
: (b) 1/2
: 4.(a) 老實說我不懂這裡要寫什麼= = u?
: (b) 0.8664
: 希望有人一起討論討論><
補充第二題的C&D
(C)
從累積分布函數出發，Fz(z)=p{max(X,Y)小於等於z}=p{x小於等於z}*p(y小於等於y)
(因為獨立)
2
=z 0<z<1
由於題目是求分布函數
0 ,if z<0
2
ANS: Fz(z)= z ,if 0<z<1
1 ,if z>1
期望值我就用密度函數作
fz(z)=2z 0<z<1
ANS: E[Z]=2/3
如果有錯還請多多指教...一大早起床頭腦還有些遲鈍XD
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