How to solve the choosing best secretary Problem for N=100?
The problem is described in detail Here
But what if we limit our N to 100 candidates?
1-If we have 100 Candidates what is the probability that you hire the best one with maximum probability?
2-how to Maximize the expected rank of hired candidate?
3-Compute the probability of success of “MyStrategy”
where MyStrategy is:
Wait till $frac{N+1}{2}$ candidate
Hire anyone with best rank so far
If no such candidate then hire the last candidate?
probability probability-theory
asked Dec 27 '18 at 12:08
Muhammad Fasiurrehman Sohi
187
|
show 1 more comment
The problem is described in detail Here
But what if we limit our N to 100 candidates?
1-If we have 100 Candidates what is the probability that you hire the best one with maximum probability?
2-how to Maximize the expected rank of hired candidate?
3-Compute the probability of success of “MyStrategy”
where MyStrategy is:
Wait till $frac{N+1}{2}$ candidate
Hire anyone with best rank so far
If no such candidate then hire the last candidate?
probability probability-theory
asked Dec 27 '18 at 12:08
Muhammad Fasiurrehman Sohi
187
see here en.wikipedia.org/wiki/Secretary_problem
– Dr. Sonnhard Graubner
Dec 27 '18 at 12:09
Not following. When you say "hire anyone with best rank so far" you appear to be allowing us to hire from the pool of rejected candidates. That is not allowed under the standard problem, and it would seem to trivialize the issue (as you could just look at all of them and pick the best).
– lulu
Dec 27 '18 at 12:13
If you meant the standard problem, then the standard solution is optimal. The fact that $frac {100}e$ isn't an integer means you have to test the two integers nearest it to see which is better.
– lulu
Dec 27 '18 at 12:14
@lulu I am confused as 100/e is not a probability .
– Muhammad Fasiurrehman Sohi
Dec 27 '18 at 12:22
@lulu i have update the question
– Muhammad Fasiurrehman Sohi
Dec 27 '18 at 12:25
|
show 1 more comment
The problem is described in detail Here
But what if we limit our N to 100 candidates?
1-If we have 100 Candidates what is the probability that you hire the best one with maximum probability?
2-how to Maximize the expected rank of hired candidate?
3-Compute the probability of success of “MyStrategy”
where MyStrategy is:
Wait till $frac{N+1}{2}$ candidate
Hire anyone with best rank so far
If no such candidate then hire the last candidate?
probability probability-theory
asked Dec 27 '18 at 12:08
Muhammad Fasiurrehman Sohi
187
The problem is described in detail Here
But what if we limit our N to 100 candidates?
1-If we have 100 Candidates what is the probability that you hire the best one with maximum probability?
2-how to Maximize the expected rank of hired candidate?
3-Compute the probability of success of “MyStrategy”
where MyStrategy is:
Wait till $frac{N+1}{2}$ candidate
Hire anyone with best rank so far
If no such candidate then hire the last candidate?
probability probability-theory
probability probability-theory
asked Dec 27 '18 at 12:08
Muhammad Fasiurrehman Sohi
187
asked Dec 27 '18 at 12:08
Muhammad Fasiurrehman Sohi
187
edited Dec 27 '18 at 12:25
asked Dec 27 '18 at 12:08
Muhammad Fasiurrehman Sohi
187
asked Dec 27 '18 at 12:08
Muhammad Fasiurrehman Sohi
187
asked Dec 27 '18 at 12:08
Muhammad Fasiurrehman Sohi
187
187
see here en.wikipedia.org/wiki/Secretary_problem
– Dr. Sonnhard Graubner
Dec 27 '18 at 12:09
Not following. When you say "hire anyone with best rank so far" you appear to be allowing us to hire from the pool of rejected candidates. That is not allowed under the standard problem, and it would seem to trivialize the issue (as you could just look at all of them and pick the best).
– lulu
Dec 27 '18 at 12:13
If you meant the standard problem, then the standard solution is optimal. The fact that $frac {100}e$ isn't an integer means you have to test the two integers nearest it to see which is better.
– lulu
Dec 27 '18 at 12:14
@lulu I am confused as 100/e is not a probability .
– Muhammad Fasiurrehman Sohi
Dec 27 '18 at 12:22
@lulu i have update the question
– Muhammad Fasiurrehman Sohi
Dec 27 '18 at 12:25
|
show 1 more comment
see here en.wikipedia.org/wiki/Secretary_problem
– Dr. Sonnhard Graubner
Dec 27 '18 at 12:09
Not following. When you say "hire anyone with best rank so far" you appear to be allowing us to hire from the pool of rejected candidates. That is not allowed under the standard problem, and it would seem to trivialize the issue (as you could just look at all of them and pick the best).
– lulu
Dec 27 '18 at 12:13
If you meant the standard problem, then the standard solution is optimal. The fact that $frac {100}e$ isn't an integer means you have to test the two integers nearest it to see which is better.
– lulu
Dec 27 '18 at 12:14
@lulu I am confused as 100/e is not a probability .
– Muhammad Fasiurrehman Sohi
Dec 27 '18 at 12:22
@lulu i have update the question
– Muhammad Fasiurrehman Sohi
Dec 27 '18 at 12:25
see here en.wikipedia.org/wiki/Secretary_problem
– Dr. Sonnhard Graubner
Dec 27 '18 at 12:09
see here en.wikipedia.org/wiki/Secretary_problem
– Dr. Sonnhard Graubner
Dec 27 '18 at 12:09
Not following. When you say "hire anyone with best rank so far" you appear to be allowing us to hire from the pool of rejected candidates. That is not allowed under the standard problem, and it would seem to trivialize the issue (as you could just look at all of them and pick the best).
– lulu
Dec 27 '18 at 12:13
Not following. When you say "hire anyone with best rank so far" you appear to be allowing us to hire from the pool of rejected candidates. That is not allowed under the standard problem, and it would seem to trivialize the issue (as you could just look at all of them and pick the best).
– lulu
Dec 27 '18 at 12:13
If you meant the standard problem, then the standard solution is optimal. The fact that $frac {100}e$ isn't an integer means you have to test the two integers nearest it to see which is better.
– lulu
Dec 27 '18 at 12:14
If you meant the standard problem, then the standard solution is optimal. The fact that $frac {100}e$ isn't an integer means you have to test the two integers nearest it to see which is better.
– lulu
Dec 27 '18 at 12:14
@lulu I am confused as 100/e is not a probability .
– Muhammad Fasiurrehman Sohi
Dec 27 '18 at 12:22
@lulu I am confused as 100/e is not a probability .
– Muhammad Fasiurrehman Sohi
Dec 27 '18 at 12:22
@lulu i have update the question
– Muhammad Fasiurrehman Sohi
Dec 27 '18 at 12:25
@lulu i have update the question
– Muhammad Fasiurrehman Sohi
Dec 27 '18 at 12:25
|
show 1 more comment
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see here en.wikipedia.org/wiki/Secretary_problem
– Dr. Sonnhard Graubner
Dec 27 '18 at 12:09
Not following. When you say "hire anyone with best rank so far" you appear to be allowing us to hire from the pool of rejected candidates. That is not allowed under the standard problem, and it would seem to trivialize the issue (as you could just look at all of them and pick the best).
– lulu
Dec 27 '18 at 12:13
If you meant the standard problem, then the standard solution is optimal. The fact that $frac {100}e$ isn't an integer means you have to test the two integers nearest it to see which is better.
– lulu
Dec 27 '18 at 12:14
@lulu I am confused as 100/e is not a probability .
– Muhammad Fasiurrehman Sohi
Dec 27 '18 at 12:22
@lulu i have update the question
– Muhammad Fasiurrehman Sohi
Dec 27 '18 at 12:25