Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and beginning April 20th, 2021 (Eastern Time) the Yahoo Answers website will be in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.
Trending News
Poisson distribution?
Let X have a poisson distribution such that 3P( x =1) = P( x=2) find P( X =4)
Tried that I get something around 22 which makes no sense.
1 Answer
- efqyLv 71 decade agoFavorite Answer
Write the formula for the Poisson probability function at x with parameter say lambda (or mu, or whatever symbol you wish for the parameter)
What is P(X=2)? (it will be a function of lambda)
What is P(X=1)? What is 3P(X=1)?
Equate the two, cancel out common terms, you get a quadratic for the parameter. Now substitute that into the p.f. to evaluate P(X=4)
--
22 is completely wrong
To save typing, I'll write in terms of the parameter mu
P(X=x) = exp(-mu) mu^x/x!
3P(X=1) = 3exp(-mu).mu
P(X=2) = exp(-mu).mu^2/2
exp(-mu).mu^2/2 = 3exp(-mu).mu
mu^2/2 = 3.mu
mu = 6
That was what I said to do - what was hard about that?
NOW evaluate P(X=4)