# [R] Sum(Random Numbers)=100

Peng Jiang jp021 at sjtu.edu.cn
Tue Jul 8 08:56:40 CEST 2008

Hi,
I am afraid there is no other way except using brute force, that
is , loop until their sum reaches your expectation.
it is easy to figure out this probability by letting their sum to be
a new random variable Z and Z = X_1 + \ldots + X_n
where X_i ~ Poisson({\lambda}_i) . By calculating their moment
generate function we can find the pmf of Z which is
a new Poisson random variable with the parameter \sum_{i}{{\lambda}_i}.

and Moshe Olshansky's method  is also correct except it is based on
the conditioning.
On 2008-7-8, at 下午1:58, Shubha Vishwanath Karanth wrote:
On 2008-7-8, at 下午2:39, Moshe Olshansky wrote:

> If they are really random you can not expect their sum to be 100.
> However, it is not difficult to get that given that the sum of n
> independent Poisson random variables equals N, any individual one
> has the conditional binomial distribution with size = N and p = 1/n,
> i.e.
> P(Xi=k/Sn=N) = (N over k)*(1/n)^k*((n-1)/n)^(N-k).
> So you can generate X1 binomial with size = 100 and p = 1/50; if X1
> = k1 then the sum of the rest 49 must equal 100 - k1, so now you
> generate X2 binomial with size = 100-k1 and p = 1/49; if X2 = k2
> then generate X3 binomial with size = 100 -(k1+k2) and p = 1/48, etc.
>
> Why do you need this?
>
>
> --- On Tue, 8/7/08, Shubha Vishwanath Karanth <shubhak at ambaresearch.com
> > wrote:
>
>> From: Shubha Vishwanath Karanth <shubhak at ambaresearch.com>
>> Subject: [R] Sum(Random Numbers)=100
>> To: r-help at stat.math.ethz.ch
>> Received: Tuesday, 8 July, 2008, 3:58 PM
>> Hi R,
>>
>>
>>
>> I need to generate 50 random numbers (preferably poisson),
>> such that
>> their sum is equal to 100. How do I do this?
>>
>>
>>
>>
>>
>> Thank you,
>>
>> Shubha
>>
>>
>>
>> This e-mail may contain confidential and/or privileged
>> i...{{dropped:13}}
>>
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>
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-----------------------------------------------
Peng Jiang 江鹏 ,Ph.D. Candidate
Antai College of Economics & Management

Department of Mathematics

Shanghai Jiaotong University (Minhang Campus)