Finding the distribution function (homework help)

Question

I do not quite understand what is classified as a distribution function and how to find a density function if one is a distribution function. For example how can I determine if the following is a distribution function? If it is, how do I find its density function? Any advice would be greatly appreciated! \begin{cases} e^\frac{-1}{x}, & \text{X > 0} \\ 0, & \text{X ≤ 0} \\ \end{cases}

Answer 1

To check if this is a distribution function you must chwck the following: 1) is it increasing? 2) is $\lim_{x \rightarrow -\infty] =0 $? 3 is $\lim_{x\rightarrow \infty}= 1?

(for your example function the answer would be yes).