# Let X_i, i=1,…,n be Geometric i.i.d random variables, which represent the number of fails, with parameter p.

How to find a probability that sum of geometric variables is less than a number
Let ${X}_{i},i=1,\dots ,n$ be Geometric i.i.d random variables, which represent the number of fails, with parameter p.
Calculate or estimate from above and below:
$P\left(\sum _{i=1}^{n}{X}_{i}\le A\right),\phantom{\rule{1em}{0ex}}A\in N.$
I know that sum of the geometric random variables is the negative binomial, but I would not know all the parameters for the negative binomial r.v.
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

kuglatid4
Step 1
You probably mean $A\in \mathbb{N}$, i.e. A is a natural number. You should probably use CLT here, as n is large, Xi are iid with $\mu <\mathrm{\infty },{\sigma }^{2}<\mathrm{\infty }$
$P\left({S}_{n}.
Step 2
Here $z=\frac{A-n\mu }{\sigma \sqrt{n}}$, and $\mu ,\sigma$ are mean and sd of each ${X}_{i}$, which you can easily find.