推 jenny200638:!!我豁然開朗!! 之前想的太差勁了>< 感謝!! 01/23 20:36
推 jenny200638:第三題的(d) 積分(0→3/2)(0→3/2-y) 2dxdy 這樣嗎 01/23 23:50
→ jenny200638:算出來的答案是不太一樣，只是範圍抓不太到想法 01/23 23:50
※ 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.
5/8 * 4/7 * 3/6 = 5/28
: (b) Balls are drawn at random with replacement until a red ball is drawn.
: What is the probability that exactly 3 drawn are required.
令X表直到抽中紅球為止所需抽取次數 X~Geo(p = 3/8)
f(x) = (3/8)*(5/8)^x-1 ,x=1,2...無限
P(X=3)= (3/8)*(5/8)^2
= 75/512
: (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.
令Y表6次抽取中 紅球的個數 Y~B(n=6,p= 3/8)
P(Y=3) = 6!/3!3! * (3/8)^3 * (5/8)^3
= 0.2575
: 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.
f(x) = 1 , 0≦x≦1
Z = X^2 , X = Z^(-1/2) , |J| = 1/[2z^(1/2)]
f(z) = 1*|J|
= 1/[2z^(1/2)] , 0≦z≦1
: (b) Find E(Z).
積分符號不會打... 總之 答案跟你一樣是 1/3
: (c) Find distribution function of W.
: (d) Find E(W).
(c)&(d)...暫時想不到 XD
: 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.
跟你一樣是 f(x) = 2x , 0≦x≦1
: (b) Calculate P(2X+2Y < 3).
這小題把限制範圍畫出來後，算出所包圍的斜線面積
再將斜線面積 * joint p.d.f (也就是2)
我算出來的答案是 0.875
: 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)
E(Xbar)= μ , Var(Xbar) = σ^2/n
當然過程是一定要寫的啦~~~~
: (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 )
雖然查表後的答案是正確的，不過題目要你用符號表示，所以還是照他說的吧
Φ(1.5)-Φ(-1.5)
: 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><
希望有高人指點一下囉~~~ 教學相長 XD
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