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Old 09-11-2014, 04:12 AM
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magdon magdon is offline
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Join Date: Aug 2009
Location: Troy, NY, USA.
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Default Re: Stuck on Problem 1.7

Your understanding is correct that each \nu has the same binomial distribution. What you are missing is that each coin is tossed independently. An example might help.

Toss the two coins 6 times and suppose the first has 3 heads and the second gas 2 heads.

\nu_1=0.5,\nu_2=\frac{1}{3}.

Define the deviations:

d_1=|\nu_1-\mu_1|=0,\ d_2=|\nu_2-\mu_2|=\frac{1}{6}.

Define the worst deviation:

d=\max_i |\nu_i-\mu_i|=\max(d_1,d_2)=\frac{1}{6}.

In this particular instance the deviation is 0.16666. You are asked to compute the probability distribution for d. In particular,

P[d>\epsilon]


Quote:
Originally Posted by foenix View Post
Greetings,

This is in reference to part (b) of Problem 1.7
I am having some difficulty understanding what is meant by using the max over two coins.

My understanding is that the two coins both have binomial distributions for nu with 6 trials and a mu of .5. As such, wouldn't the probability of a given nu be the same for both coins? What am I missing here?

Appreciate the help.
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