LFD Book Forum *ANSWER* checking the answer of Q1
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#1
10-05-2013, 05:17 PM
 eychen Junior Member Join Date: Aug 2013 Posts: 7

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?
#2
10-06-2013, 10:11 PM
 yaser Caltech Join Date: Aug 2009 Location: Pasadena, California, USA Posts: 1,478
Re: *ANSWER* checking the answer of Q1

Quote:
 Originally Posted by eychen 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 is in fact 0.1, not 1.
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#3
10-07-2013, 11:16 AM
 eychen Junior Member Join Date: Aug 2013 Posts: 7
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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