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><
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