# Statistics homework

#### Novacaine

##### New Member
Hello, I am doing an introductional statistics unit in my first semester at uni the moment. I have a question to do and I have tried it for several days, but I still did not solve it.

I have to derive a marginal distribution function for X. X is defined as the sum of N independent Bernoulli trials. N is a random variable that behaves according to a Poisson distribution. p, Lambda etc is not given, so I have to derive a general function.

#### BGM

##### TS Contributor
Have not check your whole calculation, but one reminder for you from the first line:

You have correctly stated that $$n \geq x$$ in the summation, as required in a Binomial model. Note that you are calculating the pmf

$$\Pr\{X = x\}$$

and from the whole calculation process $$x$$ is fixed from the very beginning. (And if this calculation results holds for all support point of $$X$$, then you have finished calculating the whole pmf of $$X$$)

For each fixed $$x$$, we have

$$\Pr\{N = n, X = x\} = 0$$ when $$n < x$$

Therefore all the initial terms from $$n = 0$$ to $$n = x - 1$$ vanished, and you are actually summing from $$n = x$$.

#### Novacaine

##### New Member
Oh thank you, you are absolutely right