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November 15th, 2013, 12:20 PM   #1
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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)
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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.
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November 15th, 2013, 11:08 PM   #3
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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 ?
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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?
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November 16th, 2013, 04:01 AM   #5
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Re: If a random variable x follows a Poisson distribution su

thanks so much
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October 10th, 2017, 11:54 AM   #6
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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
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October 11th, 2017, 07:58 AM   #7
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m^2= m is the same as m^2- m= m(m- 1)= 0.
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