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-   -   *ANSWER* checking the answer of Q1 (http://book.caltech.edu/bookforum/showthread.php?t=4433)

eychen 10-05-2013 06:17 PM
*ANSWER* checking the answer of Q1
 
Dear all,

For Q1, I got nu_min around 0.375. Therefore, [d] would be the closet answer.
I feel the answer is reasonable, for the following consideration:

1. The probablity of getting no head outcomes in 10 trails is 1/1024.
2. For 1000 ten-times-thrown coins, the probability of getting no one with head count = 0 is [(1024-1)/1024]^1000 = 0.375.
3. In most cases, when there is no one with head count =0, the lowest head count is most likely to be 1.
4. Therefore, the expectation value of nu_min will be approximately 0*0.625 + 1*0.375 = 0.375.

Am I doing anything wrong? Or I misunderstood the question?

yaser 10-06-2013 11:11 PM
Re: *ANSWER* checking the answer of Q1
 
Quote:
Originally Posted by eychen (Post 11528)
Dear all,

For Q1, I got nu_min around 0.375. Therefore, [d] would be the closet answer.
I feel the answer is reasonable, for the following consideration:

1. The probablity of getting no head outcomes in 10 trails is 1/1024.
2. For 1000 ten-times-thrown coins, the probability of getting no one with head count = 0 is [(1024-1)/1024]^1000 = 0.375.
3. In most cases, when there is no one with head count =0, the lowest head count is most likely to be 1.
4. Therefore, the expectation value of nu_min will be approximately 0*0.625 + 1*0.375 = 0.375.

Am I doing anything wrong? Or I misunderstood the question?
Your reasoning is both nice and correct, and the problem is just technical that when you have 1 head, the corresponding \nu is in fact 0.1, not 1. :(

eychen 10-07-2013 12:16 PM
Re: *ANSWER* checking the answer of Q1
 
Hi Yaser,

I see. nu is the fraction, not the number of the head count. Thank you! :)


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