How Do You Solve a Poisson Distribution Problem Where 3P(X=1)=P(X=2)?

[tiger2380]

Can someone help me with this question:
If X has a Poisson distribution so that 3P(X=1)=P(X=2)
find the pdf of X, and P(X=4)?

 

[robert Ihnot]

"pdf," I assume means Poisson Distribution Function.

Well, the function is $$P(n)=\frac{e^{-\kappa}\kappa^n}{n!}$$

So since we know values of n, the important thing is to find the particular value of the constant $$kappa, \kappa$$

 

[mathman]

It looks like k=6.