[R] How to solve this complex equation

[Chel Hee Lee]

The functional form given in the post written by Ssuhanchen captures my 
eyes.   It is the cumulative distribution function of Poisson when the 
number of counts is less than or equal to 2 with unknown parameter 
mu=x/2.   Since it is a nonlinear function, there may be multiple 
solutions but the solution should be greater than 0 (if I am in the 
right track).   I am assuming this functional form is originated from 
the Poisson.  Under this assumption, one solution is found as below:

 > rt <- uniroot(function(x) ppois(2, lambda=x)-0.05, interval=c(0.5,1), 
extendInt="yes")
Warning messages:
1: In ppois(2, lambda = x) : NaNs produced
2: In ppois(2, lambda = x) : NaNs produced
3: In ppois(2, lambda = x) : NaNs produced
 > ppois(2, lambda=rt$root)
[1] 0.0500001
 > rt$root
[1] 6.295791

Thus, the solution x would be rt$root*2 (Note that I did not try to find 
other solutions).  I hope this helps.

Chel Hee Lee

On 2/10/2015 2:29 AM, Rolf Turner wrote:
> On 10/02/15 14:04, Ssuhanchen wrote:
>> Hi!
>>
>> I want to use R to calculate the variable x which is in a complex 
>> equation
>> in below:
>>
>>   2
>>   Σ[exp(-x/2)*(x^k)/(2^k*k!)]=0.05
>> k=0
>>
>> how to solve this equation to get the exact x in R?
>
> Is this homework?  Sure looks like it.  Talk to your prof.  Or do a 
> bit of work on learning how to use R --- which is presumably the point 
> of the exercise.
>
> cheers,
>
> Rolf Turner
>