Probability function- Random variable

Question

I need to find a Probability function using

$$ F(x) = \begin{cases} 0 & \text{if $x<0$}\\ \frac{1-a^k}{1-a^{n+1}} & \text{if $k-1 \leq x \leq k, k=1,\dots,n, n>1$}\\ 1 & \text{if $x \geq n$} \end{cases} $$

Could someone help me with this exercise?

Thank you in advance.

Answer 1

You use a term (probability function) that I am not familiar with. Do you mean probability density function? If so, you are dealing with a discrete distribution with $p_k\gt 0$ defined for $x=k,\ 0\le k\le n$. $p_k=\frac{a^k-a^{k+1}}{1-a^{n+1}}$