View Single Post
  #2  
Old 10-06-2013, 11:11 PM
yaser's Avatar
yaser yaser is offline
Caltech
 
Join Date: Aug 2009
Location: Pasadena, California, USA
Posts: 1,477
Default Re: *ANSWER* checking the answer of Q1

Quote:
Originally Posted by eychen View Post
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.
__________________
Where everyone thinks alike, no one thinks very much
Reply With Quote