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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
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Re: If a random variable x follows a Poisson distribution su

Quote:
 Originally Posted by r-soy 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)
Poisson distribution has one parameter m. Mean and variance = m.
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
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Re: If a random variable x follows a Poisson distribution su

Quote:
 Originally Posted by r-soy thanks please I have some questions : - 1 - Is because that mean equal to 1 that mean variance = mean .
For a Poisson distribution, the mean and variance are both equal to the relative frequency. So, if you solve the equation and get the relative frequency, then you've found the mean and variance.

Quote:
 Originally Posted by r-soy 2 - in second ii) p(x grater than and equal 1 ) why in the answer written 1 -p(x less than 1 )
It's your choice. You can either sum the probabilities that x = 1 to infinity. Or, you can subtract the probability that x = 0 from 1. Which is going to be easier and quicker?

 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: 2,719 Thanks: 699 m^2= m is the same as m^2- m= m(m- 1)= 0.

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# if x is a poisson distribution such that p(x=1)=p(x=2)

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