m******t
发帖数: 273 | 1 【 以下文字转载自 Quant 讨论区 】
发信人: myregmit (myregmit), 信区: Quant
标 题: 面试题, make decision for two closed envelopes
发信站: BBS 未名空间站 (Thu Oct 3 13:00:22 2013, 美东)
An interview question:
Given two closed same envelopes, one may have $20 or $10, another one may
have $20 or $5.
You pick up one randomly and find it has $10, now you are given a chance to
make decision about whether to open another envelope.
If yes, you have to given up the $10 that you have earned and accept the
money in it no matter it is more or less than
your $10 currently in your hand.
How to make the decision ?
Any help would be appreciated.
Thanks ! |
n*****n
发帖数: 3123 | 2 No. the expected value is 12.5 if choose no, and suppose the probability of
getting 5 is uniformly distributed in (0,1). |
k*z
发帖数: 4704 | |
D*G
发帖数: 471 | 4 不应该是yes吗？
of
【在 n*****n 的大作中提到】
: No. the expected value is 12.5 if choose no, and suppose the probability of
: getting 5 is uniformly distributed in (0,1).
|
n*****n
发帖数: 3123 | 5 ft. I mean yes.
【在 D*G 的大作中提到】
: 不应该是yes吗？
:
: of
|
I*****a
发帖数: 5425 | 6 it depends on ur loss function.
to
【在 m******t 的大作中提到】
: 【 以下文字转载自 Quant 讨论区 】
: 发信人: myregmit (myregmit), 信区: Quant
: 标 题: 面试题, make decision for two closed envelopes
: 发信站: BBS 未名空间站 (Thu Oct 3 13:00:22 2013, 美东)
: An interview question:
: Given two closed same envelopes, one may have $20 or $10, another one may
: have $20 or $5.
: You pick up one randomly and find it has $10, now you are given a chance to
: make decision about whether to open another envelope.
: If yes, you have to given up the $10 that you have earned and accept the
|
m******t
发帖数: 273 | 7 Could you please use an example to explain more about how to use loss
function here ?
Thanks
【在 I*****a 的大作中提到】
: it depends on ur loss function.
:
: to
|
c******r
发帖数: 300 | 8 The follow-up is what are you going to do if you are not allowed to open the
first envelop but is told the other one is either half of the money in this
one or twice of the amount. Should you switch?
to
【在 m******t 的大作中提到】
: Could you please use an example to explain more about how to use loss
: function here ?
: Thanks
|
|
m******t
发帖数: 273 | 9 Suppose that we have X dollar in the first one, the expected value of second
one is
1/2 * X + 1/2 * 2* X = 1.5 X
So, we should switch ?
Right ?
the
this
【在 c******r 的大作中提到】
: The follow-up is what are you going to do if you are not allowed to open the
: first envelop but is told the other one is either half of the money in this
: one or twice of the amount. Should you switch?
:
: to
|
t*****w
发帖数: 254 | 10 the equation is
1/2 * 0.5*X + 1/2 * 2* X = 1.25 X
second
【在 m******t 的大作中提到】
: Suppose that we have X dollar in the first one, the expected value of second
: one is
: 1/2 * X + 1/2 * 2* X = 1.5 X
: So, we should switch ?
: Right ?
:
: the
: this
|
|
|
B****n
发帖数: 11290 | 11 If you want to maximize your expectation, then you would need to know the
probability of seeing 20 dollars in another envelope.
However, if you need 10 dollars (or money between 5 and 10) immediately, you
should not change.
So it all depends on the situation and what you want.
I believe there must be a better solution than mine, but the idea should be
similar because it's based on common sense.
to
【在 m******t 的大作中提到】
: Suppose that we have X dollar in the first one, the expected value of second
: one is
: 1/2 * X + 1/2 * 2* X = 1.5 X
: So, we should switch ?
: Right ?
:
: the
: this
|
I*****a
发帖数: 5425 | 12 just as what Bremen said
【在 m******t 的大作中提到】
: Could you please use an example to explain more about how to use loss
: function here ?
: Thanks
|
h**********1
发帖数: 155 | 13 no, the expected value would be the same.
the
this
【在 c******r 的大作中提到】
: The follow-up is what are you going to do if you are not allowed to open the
: first envelop but is told the other one is either half of the money in this
: one or twice of the amount. Should you switch?
:
: to
|
c******r
发帖数: 300 | 14 Should you switch again then?
【在 t*****w 的大作中提到】
: the equation is
: 1/2 * 0.5*X + 1/2 * 2* X = 1.25 X
:
: second
|
c******n
发帖数: 4965 | 15 la u didn't say the probability of ’may have 20 or 5’
to
【在 m******t 的大作中提到】
: Suppose that we have X dollar in the first one, the expected value of second
: one is
: 1/2 * X + 1/2 * 2* X = 1.5 X
: So, we should switch ?
: Right ?
:
: the
: this
|
m******t
发帖数: 273 | 16 They have 50% probability.
【在 c******n 的大作中提到】
: la u didn't say the probability of ’may have 20 or 5’
:
: to
|
