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#1
02-21-2015, 10:34 AM
 Andrew87 Junior Member Join Date: Feb 2015 Posts: 6
Homework Q5

Hi, I'm working on the 6-th question but I can't get the solution.

I solved Q5 and I found a probability to get on just one sample (N=10) of 0.0047. Then to compute the probability to get at least one sample with , I modeled the number of samples with 0 red marbles with a binomial random variable . Hence, the probability I need is

and

Finally , so my closest answer is [3] = 0.550, however the solution report [c] as right answer. Where did I make a mistake ? Thank you in advance for your time (and sorry for my english).
#2
02-28-2015, 07:55 PM
 yaser Caltech Join Date: Aug 2009 Location: Pasadena, California, USA Posts: 1,478
Re: Homework Q5

Quote:
 Originally Posted by Andrew87 Hi, I'm working on the 6-th question but I can't get the solution. I solved Q5 and I found a probability to get on just one sample (N=10) of 0.0047. Then to compute the probability to get at least one sample with , I modeled the number of samples with 0 red marbles with a binomial random variable . Hence, the probability I need is and Finally , so my closest answer is [3] = 0.550, however the solution report [c] as right answer. Where did I make a mistake ? Thank you in advance for your time (and sorry for my english).
I did the math and the probability that one sample has no red marbles, which is evaluates to approximately 0.00034 rather than 0.0047.
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#3
03-03-2015, 07:25 AM
 Andrew87 Junior Member Join Date: Feb 2015 Posts: 6
Re: Homework Q5

Thank you very much Prof. Yaser !

I did a mistake in calculating the probability of the Homework 4. This was caused by the fact that I used the Hoeffding inequality to compute this probability instead of a simple binomial distribution. Now, I'm wondering a more general question: is this slack between the exact probability one gets with the binomial (in this case) and the bound provided by the Hoeffding inequality typical ? Thank you very much in advance for your answer.
#4
03-03-2015, 08:47 PM
 yaser Caltech Join Date: Aug 2009 Location: Pasadena, California, USA Posts: 1,478
Re: Homework Q5

Yes. Since the bound is the same for cases that have different probabilities, it is forced to be loose in some of the cases.
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#5
03-04-2015, 04:15 AM
 Andrew87 Junior Member Join Date: Feb 2015 Posts: 6
Re: Homework Q5

Thank you very much for your answer Prof. Yaser !

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