STPM-学校功课討論区

Leong13

four rods of length  1, 2,3, and 4 units
are placed in a bag from which one rod is
selected at random. the probabilities of
selecting a rod of length l is kl.
after a rod has been selected it is not
replaced. the probabilities of selection
for each of the three rods that remain
are in the same ratio as they were before
the first selection. a second rod is now
selected from the bag. difining Y bto be
the length of this rod and writing
P1 = P ( Y=1 l X=2 )
P2 = P ( Y=2 l X=1 )
show that 16P1 = 9P2.
show also that P ( X + Y = 3 ) = 17/360

hamilan911

（1+2+3+4）k = 1
k = 1/10

P2=P(Y=2|X=1)=2/9
P1=P(Y=1|X=2)=1/8
9P2=16P1=2 - proved

P(X+Y=3) = P(X=1,Y=2) + P(X=2,Y=1) ＝ 1/8*2/10 + 2/9*1/10 = 17/360

cold_spoon

推一推，麻烦各位帮我看看贴在#405贴的问题好吗？谢谢

flash

原帖由 cold_spoon 于 3-10-2007 04:32 PM 发表
推一推，麻烦各位帮我看看贴在#405贴的问题好吗？谢谢

第一题（b）我算到是 0.560
(c) 0.089
(d) 0.098

cold_spoon

原帖由 flash 于 3-10-2007 07:10 PM 发表


第一题（b）我算到是 0.560
(c) 0.089
(d) 0.098

我刚刚才发现我的（b)的答案错了，正确的答案是0.5595,也就是你的答案是对的。(c)的答案也是对，唯有（d)的正确答案是0.2918

书的答案是
(a)0.1755
(b)0.5595
(c)0.0888
(d)0.2918

hamilan911

(c)the distribution follows Poisson distrbution with mean = 4x5 = 20
也就是 Y=4X, Y~P0(20)
所以P(Y=20) = 0.0888

(d)我找到的答案和flash兄一样，也就是利用part b 的 0.5595来power4 = 0.098

题目的意思好像有些含糊(both broken是指每天都 broken还是什么），不是很肯定

3. X~P0(1/10)
a.P(X=0) = 0.9048 = 0.90(2dp)
b.P(X>=4) = 1 - P(X=0) - P(X=1) - P(X=2) - P(X=3) = 0.00000385 = 0
c.P(X=0) = 0.95
e^(-mu) = 0.95
mu = -ln 0.95 = 0.0513
1/2t = 0.0513
t = 0.1026 minutes = 6 seconds

Leong13

樓主為什麼要加Ｄ１＝Ｄ２

Leong13

A population consists of three races A
, B, and C in the ratio 1:5:14

a. A sample of three individuals is
   selected at random from this
   population.

i)determine the probability that all
   three individuals are of different
   races.

ii)find the probability that all three
   individuals are of the same race.

b. A sample of 40 individuals is selected
   at random from the population.

i)  find an approximate value for the
    probability that four or more of
    the individuals are from race A.

ii) Find an approximate value for the
    probability that exactly ten
    individuals are from race B.

hamilan911

当D1=D2,S=0,所以D1>S

hamilan911

a
i) 1C1*5C1*14C1/20C3
ii)(5C3+14C3)/20C3

b
i)n=40, p = 0.05 , so approximate to Poisson with mu=40x0.05=2
X~P0(2)
P(X>=4) = 1 - P(X=0) - P(X=1) - P(X=2) - P(X=3) = ...

ii) n=40, p = 0.25 ,approximate to Poisson with mu=40x0.25=10
X~P0(10)
P(X=10) = e^(-10)*10^10 / 10!

Leong13

a 的答案不對
b ii 的答案也不對
書的答案
a i  = 0.0525
  ii = 0.3588

b ii = 0.1452

Leong13

The number of traffic accidents in a
town eachday has a poisson distribution
with mean 0.5 . dertermine :

a. the most likely number of traffic
    accident in a day selected at
    random.

b. the expected number of days, in
   a week selected at random , where
   no traffic accidents are recorded.

ans : a = 0 , b = 4.246

hamilan911

是ratio,没看好题目,所有的ratio都是independent的，不可以用C来做

i）3!*1/20*5/20*14/20=0.0525
ii）(5/20)^3 + (14/20)^3 = 0.358625

partb的approximation算到0.1251,没有问题

楼上那题
a)显然0.5^x / x! < 1 for x>=1
所以答案是0

b)P(X=0) = e^-0.5*0.5^0 / 0 = 0.6065
一星期所以要乘7
expected number = 0.6065*7 = 4.246

Leong13

為什麼ratio不能用Ｃ

a 我不大明白，可以解試一下嗎？

hamilan911

每个人属于哪个种族的probability都是independent的,因为那个并不是数量，是1：5：14，不是1个，5个，14个

a说明的是 e^-0.5*0.5^0 / 0! 是最高的
道理很简单，就因为0.5^0/0! = 1 , 大过所有的 0.5^x / x! where x>=1

Leong13

我明白了，thank you

Leong13

1. an electrical appliance shop has 4
   television sets for rental on a monthly
   basis. the number of televisions
   requested by customers in one month
   follows a poisson distribution with
   mean  3

i) find the expected number of television
   sets that are rented out to customers
   in a month.

2. for an automatic telephone exchange
   system, the probability of a call
   being incorrectly connected is 0.001

i) determine the minimum number of
   independent calls needed so that the
   probability that no calls are connected
   incorrectly is not more than 0.1.

[ 本帖最后由 Leong13 于 10-10-2007 05:33 PM 编辑 ]

Leong13

the number of accidents that occur in a
factory follows the poisson distribution
with a mean of 3 accidents a year. find
the probability that a year from five
years selected at random, is accident-free.

flash

原帖由 Leong13 于 10-10-2007 06:21 PM 发表
the number of accidents that occur in a
factory follows the poisson distribution
with a mean of 3 accidents a year. find
the probability that a year from five
years selected at random, is ac ...

不是很了解你的题目，你是不是要找 5 年里面，仅有一年是 accident free？如果是的话，那答案应该是 0.2366

lavendar_o5

The amount of petrol x, in thousand litres, sold in a day by a petrol station is a random variable with p.d.f

f(x)=(1/243)*(x^2-18x+81) , 0 <= x <= 9

Find the expected amount of petrol sold by the petrol station in 30 days.

我的答案是 (2.25 * 30)，对吗？