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November 15th, 2013, 12:20 PM  #1 
Senior Member Joined: Oct 2009 Posts: 895 Thanks: 1  If a random variable x follows a Poisson distribution such
How I can solve this one If a random variable x follows a Poisson distribution such that p(x=1) = 2 p (x=2) Find :  mean and variance ii) p(X greater and equal 1) iii) p(X = 3) 
November 15th, 2013, 01:25 PM  #2  
Global Moderator Joined: May 2007 Posts: 6,528 Thanks: 589  Re: If a random variable x follows a Poisson distribution su Quote:
P(x=1) = exp(m)m, P(x=2) = exp(m)(m^2)/2. So your equation becomes: m = m^2, so m = 0 or 1. I'll leave you the rest as an exercise.  
November 15th, 2013, 11:08 PM  #3 
Senior Member Joined: Oct 2009 Posts: 895 Thanks: 1  Re: If a random variable x follows a Poisson distribution su
thanks please I have some questions :  1  Is because that mean equal to 1 that mean variance = mean . 2  in second ii) p(x grater than and equal 1 ) why in the answer written 1 p(x less than 1 ) 3  when we write 1 p(x less than 1 ) , Is for atleast and as above case ? 
November 16th, 2013, 12:45 AM  #4  
Senior Member Joined: Jun 2013 From: London, England Posts: 1,316 Thanks: 116  Re: If a random variable x follows a Poisson distribution su Quote:
Quote:
 
November 16th, 2013, 04:01 AM  #5 
Senior Member Joined: Oct 2009 Posts: 895 Thanks: 1  Re: If a random variable x follows a Poisson distribution su
thanks so much

October 10th, 2017, 11:54 AM  #6 
Newbie Joined: Oct 2017 From: Lago, Nigeria. Posts: 1 Thanks: 0 
hi i am kinda confused here cause i have got a question like this to solve so how does m=m^2 ==> m = 1 or 0

October 11th, 2017, 07:58 AM  #7 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,198 Thanks: 872 
m^2= m is the same as m^2 m= m(m 1)= 0.


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distribution, poisson, random, variable 
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