p***y
发帖数: 32 | 1 One man is giving out two checks to his sons. The exact amount of money is
unknown, but one check is ten times as big as the other. Say, one is $10000
and the other is $1000.
Now when one son get one of the check and it is, say, $1000. He thinks there
are two possiblities his brother would get, either $10000 or $100. So swap is
good to him since the expectation is ($10000 + $100) /2 > $1000.
However, the other son got the same idea.
The dilemma is, how can both party think swapping is a winning | x******g
发帖数: 318 | 2 1.在自然数集上没有等概率分布
2.在不知道数值的情况下，期望值不是一个确定的数
【在 p***y 的大作中提到】
: One man is giving out two checks to his sons. The exact amount of money is
: unknown, but one check is ten times as big as the other. Say, one is $10000
: and the other is $1000.
: Now when one son get one of the check and it is, say, $1000. He thinks there
: are two possiblities his brother would get, either $10000 or $100. So swap is
: good to him since the expectation is ($10000 + $100) /2 > $1000.
: However, the other son got the same idea.
: The dilemma is, how can both party think swapping is a winning
| B****n
发帖数: 11290 | 3 應該說期望值是可以定義的 只是哥哥和弟弟都不知道
因為在已經給完錢之下 他們都不知道多或少的機率 也就是
不知道錢是對方的十分之一的機率是零還是一
只知道是這兩者之一
$10000
there
is
【在 x******g 的大作中提到】
: 1.在自然数集上没有等概率分布
: 2.在不知道数值的情况下，期望值不是一个确定的数
| x******g
发帖数: 318 | 4 我没看懂你说的
但我想你肯定有些地方说错了
比如概率是1还是0这个地方
期望值确实是可以定义的,比如我以19/2(20)^|n|概率赋予(10^n,10^(n+1))(n=+-1,+-2..)
(但是不可能赋予等概率(利用可数可加性))
但是这样定义的一个分布就不能在按照题目中的推理来进行了
总之，题目是一个恙缪
【在 B****n 的大作中提到】
: 應該說期望值是可以定義的 只是哥哥和弟弟都不知道
: 因為在已經給完錢之下 他們都不知道多或少的機率 也就是
: 不知道錢是對方的十分之一的機率是零還是一
: 只知道是這兩者之一
:
: $10000
: there
: is
| w**a
发帖数: 1024 | 5 in bayesian statistics, this is no problem.
you need specify a a prior distribution, then you will have no dilemma any
more.
is
【在 p***y 的大作中提到】
: One man is giving out two checks to his sons. The exact amount of money is
: unknown, but one check is ten times as big as the other. Say, one is $10000
: and the other is $1000.
: Now when one son get one of the check and it is, say, $1000. He thinks there
: are two possiblities his brother would get, either $10000 or $100. So swap is
: good to him since the expectation is ($10000 + $100) /2 > $1000.
: However, the other son got the same idea.
: The dilemma is, how can both party think swapping is a winning
|
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