数学M/S Paper 2讨论专区

peaceboy

回复 358# 數學神童


    画了graph然后减lor - -

hongji

回复  hongji


    0.25-0.05(0)+0.25-0.05(1)+0.25-0.05(2)+0.25-0.05(3) +a +a =1
0.7+2a =1
a= 0 ...
peaceboy 发表于 10-3-2011 10:31 PM

哎呀我只是谢写a+a=1
原来全部都要
弄到b也错了TT

hongji

2)in how many ways can odd numbers greater than 4000 be formed from the digits 1,2,4 and 8 if the digits can only be used once?



5)find the number of ways 9 people can be divided into
a)2 groups of 6 people and 3 people
b)3 groups of 4,3 and 2 people

peaceboy

回复 363# hongji


    2)in how many ways can odd numbers greater than 4000 be formed from the digits 1,2,4 and 8 if the digits can only be used once?

2+2 = 4



5)find the number of ways 9 people can be divided into
a)2 groups of 6 people and 3 people
9C6

b)3 groups of 4,3 and 2 people
9C4*5C3

hongji

13)a committee consisting of 5 people is to be selected from 6 from Six prefects and 4 form Five prefects.
find the probability that
a)at least 4 form Six prefects are chosen
b)at least one of form Five prefect is chosen















9)from a set of seven cards numbered 1 to 7 , two cards are drawn at random .
find the probability that
a)the sum of the numbers is less than 6
b)both the number are odd
c)the sum of the number is less than 6 or both the numbers are odd

hongji

bag A contains 5 red cubes and 3 blue cubes while bag B contains 4 red cubes and 7 blue cubes .A cubes is selected at random from bag A and placed in bag B , and a cube is then selected randomly from bag B.
Events B1 , M1 ,B2 ,M2 are defined as follows :
B1 : the cube placed into bag B is blue
M1 :the cube placed into bag B is red
B2 :the cube selected form bag B is blue
M2 :the cube selected form bag B is red
Find

P(B2)怎样做啊。。




P(D)=1/4  ,P(E)=2/3 and P(D  l  E)=1/3 , find P(D n E')

peaceboy

回复 365# hongji


   13)a committee consisting of 5 people is to be selected from 6 from Six prefects and 4 form Five prefects.
find the probability that
a)at least 4 form Six prefects are chosen6C4*4C1 / 9C5



b)at least one of form Five prefect is chosen




1- (6C5 / 9C5)





9)from a set of seven cards numbered 1 to 7 , two cards are drawn at random .
find the probability that
a)the sum of the numbers is less than 6
S<6 , 1+2 , 1+3,1+4,2+3
4/7C2

b)both the number are odd
(4*3/2!) / 7C2

c)the sum of the number is less than 6 or both the numbers are odd
4/7C2 + (4*3/2!) / 7C2 - 1/7C2

peaceboy

回复 366# hongji


   bag A contains 5 red cubes and 3 blue cubes while bag B contains 4 red cubes and 7 blue cubes .A cubes is selected at random from bag A and placed in bag B , and a cube is then selected randomly from bag B.
Events B1 , M1 ,B2 ,M2 are defined as follows :
B1 : the cube placed into bag B is blue
M1 :the cube placed into bag B is red
B2 :the cube selected form bag B is blue
M2 :the cube selected form bag B is red
Find

P(B2)怎样做啊。。

P(B2) = P(B1 n B2) + P(M1 n B2)         = 5/8*5/12 + 3/8*8/12



P(D)=1/4  ,P(E)=2/3 and P(D  l  E)=1/3 , find P(D n E')


P(D l E) = P(D n E) / P(E)
           = 1/3
P(D n E) / (2/3)  = 1/3
P(D n E) = 2/9
P(D n E') + P(D n E) = P(D)
P(D n E') + 2/9 = 1/4
P(D n E') = 1/4 - 2/9
             = 1/36

hongji

回复 368# peaceboy


   除了你还真的没人解TT   p(neither S nor R)=7/25  是什么意思 是 P(SnR)还是P(SuR)啊？

hongji

还有一题><

the random variable X1 ,X2 ,....,Xn are independent and each has a normal distribution with mean (U) and variance 1 . the random variable X(sample x) is defined to be (X1 + X2 +...+Xn)/n.determine,in terms of n,the value of c such that when mean(U)=0 , the probability of X(sample x) exceeding c is 0.05.
for this value of c it is desired that the probability of X(sample x) being less than c when mean(U) =0.2 should be at most 0.10.
calculate the smallest possible value of n which satisfies this requirement.


如果不明白看不懂的话
没关系
answer is c=1.645/(squareroot) n   , n=215

peaceboy

回复 369# hongji


    P(SUR)'

peaceboy

回复 370# hongji


   
the random variable X1 ,X2 ,....,Xn are independent and each has a normal distribution with mean (U) and variance 1 . the random variable X(sample x) is defined to be (X1 + X2 +...+Xn)/n.determine,in terms of n,the value of c such that when mean(U)=0 , the probability of X(sample x) exceeding c is 0.05.


answer is c=1.645/(squareroot) n   , n=215

sample variance = 1/n
P(x>c) = 0.05
P(z> c/ [(1/n)^(1/2)] = 0.05
P(z> 1.645) = 0.05
by comparison
c/ [(1/n)^(1/2)] = 1.645
c= 1.645 / n^(1/2)


for this value of c it is desired that the probability of X(sample x) being less than c when mean(U) =0.2 should be at most 0.10.
calculate the smallest possible value of n which satisfies this requirement.

mean = 0.2
P(x<c)<=0.1
P(x< 1.645 / n^(1/2)) <=0.1
P(z< {[1.645 / n^(1/2)] - 0.2}  /  [(1/n)^(1/2)] ) <=0.1
P(z< 1.645-0.2n^(1/2)) <=0.1
P(z< - 1.281) <=0.1

by comparison ,
1.645-0.2n^(1/2) <= -1.281
2.926<= 0.2n^(1/2)
n^(1/2) >= 14.63
n>=214.03
n=215

hongji

回复 372# peaceboy


    wah好厉害o..

关于point estimation的


find the population mean (U) and population variance :
1)given that X=67 + 3u , and Efi=100 , Efiui=15 , Efiui^2 =97



2)n=50,E(xi-52)=-50 , E(xi-52)^2 =1400  [这题我找到variance不会找mean,why mean不是52而是51.。。]



还有什么是parameter?

peaceboy

回复 373# hongji


    看不懂你的符号　－－

http://en.wikipedia.org/wiki/Parameter

hongji

回复  hongji


    P(SUR)'
peaceboy 发表于 17-3-2011 11:29 PM

    如果是P(SUR)=P(S)+P(R)-P(SnR)
   那么同样的
    P(SUR)'=P(S)'+P(R)'-P(SnR)'

P(R)=3/5  , P(R  l  S) =2/3 and P(SUR)' = 7/25
我要找它的P(S)是多少
我只找到..P(SUR)

peaceboy

回复 375# hongji


    P(SUR)' = 1- P(SUR)

hongji

回复 376# peaceboy


    这个我找了1-7/25=18/25P(SUR)
     18/25=3/5+P(S)-P(RnS)






通过P(SUR)能怎样找P(RnS)

peaceboy

回复 377# hongji


   
P(R)=3/5  , P(R  l  S) =2/3 and P(SUR)' = 7/25
我要找它的P(S)是多少
我只找到..P(SUR)

P(RnS) /P(S) = 2/3

1- P(SUR) = 7/25
1- [P(S) + P(R) - P(SnR)] = 7/25
1- P(S) - 3/5 +P(SnR)= 7/25
P(SnR)- P(S)= 7/25 - 2/5
                 = - 3/25
P(S) = P(SnR) +  3/25

P(RnS) /P(S) = 2/3
P(RnS)  /[P(SnR) +  3/25] = 2/3
3P(RnS) = 2[P(SnR) +  3/25]
3P(RnS)  - 2P(SnR) = 6/25
P(SnR) =6/25

P(S) = 6/25 +  3/25
       =9/25

hongji

如果我做的答案好像correlation coefficient r
是0.1667
而对的答案是0.1669
2个都可以是对的吗

peaceboy

回复 379# hongji


    应该算对吧，因为如果中途你有round off 了答案会有偏差的
所以中途通常我们用fraction，不用小数
到最后一个步骤才用calculator 算小数点
答案应该有接受一点偏差的