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Leong13

我又有問題要問
lim     ( x - modulus x )/x
x-->0^-

~Lucifer~

x-->0^-是讲x从negative axis接近0吗？如果是这样的话，我的答案是2。。。不肯定，请其他高手发表意间吧

Leong13

對，請問怎樣做？

yawchoong

原帖由 Leong13 于 26-9-2007 08:02 PM 发表
我又有問題要問
lim     ( x - modulus x )/x
x-->0^-

haha,这是negeri sembilan trial 的问题吧？
是2，continuous

cold_spoon

麻烦各位指教一些关于discrete probability distributions的问题。谢谢。

1.A motorcar repair workshop tows in an average of 5 damaged cars per week. Assuming that the number of damaged cars towed per week follows a Poisson distribution, find the probability that
a) exactly 5 cars are towed in a particular week,
b) at least 5 cars are towed in a particular week,
c) exactly 20 cars are towed in a 4-week period,
d) for 4 succesive weeks, at least 5 cars are towed in each week.

第一题我找到答案0.1755,第二个是0.6156。过后第三和四个就不会做了。


2.The probability that either of 2 furnaces in a factory breaks down on a single day is 0.02. Find the probabilities that in a week of 7 days,
a)neither furnace breaks down
b)one break down
c)both break down
In a year taken as 52 weeks, calculate the expected number of weeks that both furnaces break down at least once in a period of one week


3.The number of vehicles arriving at a petrol kiosk at any time interval t minutes has a Poisson distribution with mean 1/2t minutes. Suppose the kiosk attendant leaves the kiosk unattended for 5 minutes. Calculate, to 2 decimal places, the probability that there are
a) no vehicle arrivals
b) 4 or more vehicles arrival.
Find the maximum length of time in seconds for which the attendant could be absent with a 0.95 probability of not missing an arrival.

Leong13

我不知到，這題是我做練習的題目，請問可以explain嗎？

hamilan911

lim (x->0-) (x - |x|)/x = lim (x->0-) 1 - |x|/x = 1 - (-1) = 2

Leong13

請問 |x|)/x 一定＝﹣１嗎？

Leong13

dertermine if each of the following is a probability density function
a. P ( X=x ) = { (1+x)/2,  x= -1, 0, 1
                     0  ,  otherwise


b. f (x) = { (1+x)/2,  -1≤x≤1
                 0  ,  otherwise

Leong13

a fair dice is rolled once . if the score is 3 or more, then the " result " X is the score. if the score is 1 or 2, then the dice is rolled once agian and the " result" X is the sum of the scores of the two rolls. show that P ( X=6 ) = 2/9 and P ( X=7 ) = 1/18
the procedure is repeated 6 times and N is the number of times the result 6 or 7 is obtained. find E(N) and var ( N ) .
find P ( N =4 ).

hamilan911

不一定，但因为 x approach 0 from negative,所以会得到－1

hamilan911

a.找出P(X=-1)、P(X=0)、P(X=1)，然后加起来，不等于1，所以不是probability density function
b.integrate f(x) from -1 to 1,等于1，所以是

410楼的
P(X=6)=一次拿6+两次的和拿6（1、5和2、4=1/6+1/6*1/6+1/6*1/6=2/9
P(X=7)=两次的和拿7（1、6和2、5）=1/6*1/6+1/6*1/6 = 1/18

E(N)=np=(2/9+1/18)*6 = 5/3
Var(N)=npq=5/3*13/18=65/54

p=5/18 q=13/18
P(N=4) = 6C4 (5/18)^4 (13/18)^2 = 0.04658

Leong13

上面兩題我明白了thank you 。

如果方便可以幫我solve３７８樓的問題嗎？

[ 本帖最后由 Leong13 于 30-9-2007 09:51 PM 编辑 ]

Leong13

Two fair dice are rolled and the numbers
obtained are D1 and D2. In a game, the
score S is the smaller of the two
numbers D1 and D2 unless D1 = D2 when
the score would be 0.
Obtain the probability distribution for S.
Show that the expexted value of S is 35/18.
Find the variance for S .
Find ( D1 > S) .
the total score, T, obtained by a player is
fiven by T= S1 + 2S2 + 3S3 where S1, S2 and
S3 are the scores obtained as described above,
for three successive throws of the two dice.
Determine the expected value of T, and sho that
the variance of T is 4655/162.

hamilan911

P(S=0) = 6/36
P(S=1) = 10/36
P(S=2) = 8/36
P(S=3) = 6/36
P(S=4) = 4/36
P(S=5) = 2/36

E(S) = sum {s*P(S=s)} = 35/18
Var(S)=E(S^2)-[E(S)]^2 = sum {s^2*P(S=s)} - [E(S)]^2 = 210/36 - (35/18)^2 = 665/324

是找P(D1>S)吧？
P(D1>S)其实就是当D1=D2 所以等于1／6

T = S1+2S2+3S3
所以E(T) = E(S1)+2E(S2)+3E(S3) = 6E(S) = 6*35/18 = 35/3
Var(T) = Var(S)+2^2*Var(S)+3^2*Var(S) = 14Var(S) = 14*665/324 = 4655/162

Leong13

是找 P ( D1 > S )
不過答案不是１／６
答案＝７／１２

還有請問這句是the socre S is
the smaller of the two numbers
D1 and D2旨它們的difference 嗎？

[ 本帖最后由 Leong13 于 1-10-2007 06:50 PM 编辑 ]

hamilan911

D1,D2是指两次所得的数目,而D1并不一定>=D2，我误会了

所以P(D1>S) = P(D1>min{D1,D2}] + P(D1=D2) = 15/36 + 1/6 = 7/12

Leong13

可以解試Ｓ嗎，我不是很明。

hamilan911

S= min{D1,D2} if D1=/=D2 ,0 if D1=D2

例子:
D1=2、D2=5,那么S=2
D1=D2=3,那么S=0
D1=6,D2=4,S=4

Leong13

可是我不明白為什麼要＋ Ｄ１＝Ｄ２