# Issue with sum of probabilities of probability distribution function of a geometric random variable

Is it possible that the sum of probabilities of geometric distribution for "$$k = 1,...,n$$", where k is number of trials until the first success, is not equal to 1?

I'm asking this, because I encounter a problem, when writing a program in a language, like Matlab, it's Scilab, and I observe that for probability $$p = 0.6$$, and $$n = 10$$ I do not get the sum of probabilities equal to $$1$$ (but very close to 1). Also, I noticed that the first value for cumulative distribution function is $$0.6$$, while using Matlab function cdfgeo, the first value is $$0.84$$, which gives the right result. So, is it possible that the sum of probabilities be not $$1$$?

As additional information, I use the formula: $$P_{X}(x) = (1-p)^{k-1}p$$ where $$X$$ is a geometric random variable, $$p = \text{probability}$$, and $$k = \text{number of trials}$$.

Note that $k$ can take on any positive integer value; it is not limited just up to $10$.
• Yes. If you go up to $10$ and then stop, your probabilities would add up to somewhat less than $1$. Commented May 4, 2015 at 20:22