数学T paper 2讨论专区

darksider

原帖由 menglee 于 2009/9/23 10:46 PM 发表
E(X)=integrate 1 to 3      3/4 x(x-1)(3-x)   = 2
X1=X2=X
E(X1 +2X2) =E(X+2X)=E(3X)=3E(X)=6
问题很奇怪，唯有这样才能做到答案。
为什么突然跑出X1和X2？

X1 and X2 are independent events.
So E(x1) + 2E(x2) = 3E(x2) = 3E(x1)

So what is independent and mutually exclusive?


Mutually Exclusive
Let say I want to toss a dice.
P(getting 6 or 1) = P (getting 6) + P(getting 1)

In this case, P(getting 6) and P(getting 1) are mutually exclusive which means if you get 6, you cannot get 1 and vice versa ( P(getting 6 and getting 1) = 0).
Hence, for mutually exclusive event, you add up their probability.
Mutually exclusive event cannot be independent. (if dice shows up 1 , then P(getting 6) = 0 , it affects the probability of getting 6)

Independent
Let say I toss two die, and I want to find the probability of getting 6 in the first toss and 1 in the second toss.

P( 6 in first toss and 1 in the second toss) = P(6 in first toss) x P( 1 in second toss)

You see, both events are not mutually exclusive, ie, you can get 6 in the first toss and at the same time, you can get 1 in the second toss too.

Both events are independent of each other which means if you get 6 in the first toss, the P(1 in second toss) is also 1/6, not affected.

Hence, we multiply for independent events. P(A n B) = P(A) x P(B)
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These are not so related to the term 'independent' in finding expected number.

Expected number is mean of a set of data. Since X1 and X2 are independent of each other and they are of the same probability density function, then their expected number (mean, lambda) must be the same. Got it?

meiling

谁可以教一教probability？
我每次不知道遇到什么样的题目要用什么方法。。

四月一日的小皮

In a certain city . records for burglaries show that the probability of an arrest in one week is 0.42 .The probability of an arrest and conviction in that week is 0.35.
(a) Find the probability that a person arrested for a particular week for burglary will be convicted

a)P(a person convict | person is arrested) = 0.35/0.42 = 5/6
对吧？
可是skema给的答案是。。。0.42x0.35 = 0.147

恩儿

Q:the total supply of sugar to the town is 2600kg in August.Find the probability that there is a shortage of the sugar in the town in August.

我想问应该用P(X>2.6)还是P(X<2.6)找答案？？

darksider

题目要的是shortage (缺少）。。所以我们得找 P(X < 2600kg) given that X is the mass of sugar supply.

darksider

原帖由 四月一日的小皮 于 2009/11/26 02:37 PM 发表
In a certain city . records for burglaries show that the probability of an arrest in one week is 0.42 .The probability of an arrest and conviction in that week is 0.35.
(a) Find the probability that  ...

-records for burglaries show that the probability of an arrest in one week is 0.42 => P(arrest) = P(A) = 0.42

-The probability of an arrest and conviction in that week is 0.35 => P(convicted | arrest) =P(B|A)= 0.35 ; P(convicted) = P(B)

(a) Find the probability that a person arrested for a particular week for burglary will be convicted

=> we are required to find the probability that arrest and conviction occur together so we should find
P(AnB).

P(AnB) = P(A) x P(B|A) = 0.42 x 0.35

*Why in (a) we should find P(AnB) and not P(B|A) ?
* The burglar must be arrested first before he can be convicted of the crime. So when the question states ' the probability of an arrest and conviction in that week is 0.35' , it meas that P(arrest | conviction) = 0.35 and not P(arrest and conviction ) = 0.35
*Not a good question as it can easily mislead candidates.

星星之玲

我想请问一下哪个VECTOR 的那一课啊.....有时候会叫我们找SHORTEST DISTANCE...那个要怎样看啊? 我每次都不会看....

恩儿

可是答案给大过。。。。。怎么样？
槟华的trial paper question.

darksider

原帖由 恩儿 于 2009/11/29 03:19 PM 发表
可是答案给大过。。。。。怎么样？
槟华的trial paper question.

照理来讲一定是 P(X<2600kg),都说shortage了吗。
如果找P(X>2600kg),那就是over supply.

darksider

原帖由 星星之玲 于 2009/11/29 01:47 PM 发表
我想请问一下哪个VECTOR 的那一课啊.....有时候会叫我们找SHORTEST DISTANCE...那个要怎样看啊? 我每次都不会看....

当两个vectors are perpendicular to each other,他们之间的距离是the shortest distance.

我们就利用dot product来找出那个t(过后substitute进去equation of displacement,aSb) 或者我们画图过后用trigonometric ratio来找出shortest distance

dot product
A . B = |A| |B| cos theta; theta is angle btw the vectors. if theta = 90 , ie A and B are perpendicular to each other, A.B = 0.

idontwant2b

请问画ogive的时候可以x-axis的value如果太大可以用 --/v--- 吗？还是不从零开始？

很久没有做这种问题了，突然想到。

menglee

对，照理是没问题的。

laiverson

兩個問題：
ungrouped data 的 median, interquartile range 怎么找？
P(X>x)= ... 是 pdf 還是 cdf?

meiling

ungroup data的用算的，一个一个算
P(X>x)是opposite of F(X=x) 所以是cdf

laiverson

謝謝...
祝大家靠math t paper2 順利...

darksider

原帖由 laiverson 于 2009/12/1 11:04 AM 发表
兩個問題：
ungrouped data 的 median, interquartile range 怎么找？
P(X>x)= ... 是 pdf 還是 cdf?

ungrouped data...用stem and leaf diagram把他们排起来，过后找 (n+1)/2 th term.如果n is odd的话,那么(n+1)/2 th term就是median,如果n is even, then u find average between the two values.

interquartile...先找upper quartile ( (3/4) (n+1) ) th term. 过后找 lower quartile (1/4)(n+1) th term.

interquartile range = Q3 - Q1

F(X) = P(X </=  x) = 1 - P(X>x)

eg
pdf = P(X=x) = a , 0<x<2
                       = 0 , otherwise

cmf = P(X<x) = 0, x<0
                       = ax+b , 0<x<2
                       = 1 , x>2

kenchuan

prove tat for all values of 0(deta)

sin0(cos 20+cos40+cos 60)=cos40sin30

0 is deta.

how to solve tis question?

walrein_lim88

回复 98# kenchuan



第一: Use Cos P + cos Q = 2cos[0.5(P+Q)]cos[0.5(P-Q)]
第二: Use Cos 2A = 1 - 2sin^2 A
第三: remember this formula : sin 3A = 3sin A - 4sin^3 A ** Proving ..refer to this : http://cforum4.cari.com.my/viewthread.php?tid=1820263&;extra=page%3D1

harry_lim

回复 99# walrein_lim88
我的天～你居然会math T 2的～
我看你的math S可以拿4.0了^^

walrein_lim88

回复 100# harry_lim

你的反应酱大。。。还好啦。。PAISEH