 My Math Forum If a random variable x follows a Poisson distribution such
 User Name Remember Me? Password

 Algebra Pre-Algebra and Basic Algebra Math Forum

 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: 6,761
Thanks: 696

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
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:
 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: 3,264 Thanks: 902 m^2= m is the same as m^2- m= m(m- 1)= 0. Tags distribution, poisson, random, variable Search tags for this page
,
,

,

,

,

,

,

,

,

,

,

,

,

,

# content

Click on a term to search for related topics.
 Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post mrvp Advanced Statistics 0 January 28th, 2012 01:51 PM 450081592 Advanced Statistics 3 January 25th, 2012 11:16 PM Singularity Advanced Statistics 2 November 9th, 2011 08:11 PM meph1st0pheles Advanced Statistics 0 February 27th, 2010 02:03 PM alfangio Advanced Statistics 1 March 17th, 2009 01:46 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top

Copyright © 2019 My Math Forum. All rights reserved.      