w******g
发帖数: 67 | 1 【 以下文字转载自 JobHunting 讨论区 】
发信人: wyizhang (MM), 信区: JobHunting
标 题: 一道概率题目
发信站: BBS 未名空间站 (Thu Aug 26 19:53:59 2010, 美东)
A,C are iid random numbers uniformly distributed in (0,1)
B is random number uniformly distributed in (1/2,1)
What is the probability P(A>B,A>C)?
My answer is (1/2)*(3/8)=3/16. Is it correct? Thanks. |
c**********e
发帖数: 2007 | 2 5/24. Notice A>B and A>C are not independent.
It is an 3-D integration. |
w******g
发帖数: 67 | |
t********s
发帖数: 54 | 4 Is it
\int_{1/2}^{1}db\int_{0}^{1}dc\int_{max(b,c)}^{1}da
I got 5/48 instead of 7/24 |
s*******u
发帖数: 35 | 5 should be 5/24. You forgot to multiply by 2 which is the density of the
distribution of B.
【在 t********s 的大作中提到】
: Is it
: \int_{1/2}^{1}db\int_{0}^{1}dc\int_{max(b,c)}^{1}da
: I got 5/48 instead of 7/24
|
f***a
发帖数: 329 | 6 恩，5/48
具体点就是 P(A>B,A>C)=P(A>C>=B)+P(A>B>=C>1/2)+P(A>B>1/2>=C)
前两项明显是一样的，都是1/48，最后一项是1/16，一加是5/48.
【在 t********s 的大作中提到】
: Is it
: \int_{1/2}^{1}db\int_{0}^{1}dc\int_{max(b,c)}^{1}da
: I got 5/48 instead of 7/24
|
c**********e
发帖数: 2007 | 7 You are right. It is 5/24.
【在 s*******u 的大作中提到】
: should be 5/24. You forgot to multiply by 2 which is the density of the
: distribution of B.
|
f***a
发帖数: 329 | 8 。。。。我也忘了 -_-|
【在 s*******u 的大作中提到】
: should be 5/24. You forgot to multiply by 2 which is the density of the
: distribution of B.
|
t********s
发帖数: 54 | |
b*****8
发帖数: 37 | 10 There must have other conditions such as independence. Otherwise, all your
calculation may not be valid. For example, What if A=C? The probability is 0
.
【在 w******g 的大作中提到】
: Thanks. I got it.
|
g****s
发帖数: 181 | 11 我算出来是1／4。
A&C<1/2, 2
A|C<1/2, 2x2=4
A&C>1/2, 3x2x1=6
总共有12种可能性
A>B,A>C
C<1/2, B
C>1/2, B
so (1+2)/12=1/4
有错请指出，谢谢 |
r*****k
发帖数: 35 | 12 我得到5/24
P(A>B,A>C)=P(A>max(B,C))
令Z=max(B,C),得到f(z)=4z-1, 0.5
因此A，Z的联合分布是 f(a,z)=4z-1，0.5
然后对A，Z做二重积分，对给定Z=z，A的区间是z到1 |
o****p
发帖数: 162 | 13 By looking at all above results and voting algorithm, its 5/24.
【在 w******g 的大作中提到】
: Thanks. I got it.
|
