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August 17th, 2012, 11:51 AM  #1 
Newbie Joined: Aug 2012 Posts: 7 Thanks: 0  Independent trials of a random experiment
Let p(k) denote the probability of exactly k successes in n independent trials of a random experiment in each of which the probability of a success is p. Show that [attachment=0:311jkpf6]#13.JPG[/attachment:311jkpf6] where q=1p. Hence find the most probable number of successes when n=16 and p=0.2 I get that I must use Binomial distribution, but then what next? Please help.. 
August 18th, 2012, 05:35 AM  #2 
Senior Member Joined: Aug 2012 Posts: 229 Thanks: 3  Re: Independent trials of a random experiment
Hey UnscaryMidnight. How many combinations of ways can you get ksuccesses in n independent trials? What about in k+1 trials? What's the ratio of the two (remember you have two probability statements: one concerning getting k+1 successes and another getting ksuccesses both for n trials)? 
August 19th, 2012, 09:49 AM  #3 
Newbie Joined: Aug 2012 Posts: 7 Thanks: 0  Re: Independent trials of a random experiment
sorry, im still struggling here. Could you do an example please?

August 19th, 2012, 05:38 PM  #4 
Senior Member Joined: Aug 2012 Posts: 229 Thanks: 3  Re: Independent trials of a random experiment
p(k) and p(k+1) are probabilities for getting k and k+1 successes from n trials. You know the PDF of a binomial so try calculating the ratio of these two expressions.


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