Generate an Exponential distribution
Analyze its statistics

Rate of event occuring is λ, the reciprocal of the average arrival/wait time, t: λ=1/t. Ex. t=10s, λ=.1
Rate of thing existing is λ, the reciprocal of the average number of things per unit area/space, n: λ=1/n. Ex. n=10 things, λ=.1

Exs. coin flip is a head: λ=.5     die roll is a 6: λ=.166666     next digit of normal number is d: λ=.1     card is suit s: λ=.25

Probability of non-occurence decreases exponentially with time.
    pdf(x)= λe^-λx

Probability that the event happens in no more than (i.e. within) x amount of time or the probability that there is at least 1 thing in x area/space units:
    CDF(x) = P[X≤x] = 1-e^-λx
Probability that the event happens in at least (i.e. after) x amount of time:
    1-CDF(x)=P[X>x]= e^-λx

Given a probability percentile 0≤p≤1, what is the time x: Quantile InverseCDF Q(p)= -ln(1-p) / λ

Rate of happening/occuring/existing λ:

μ= 1/λ = average wait/arrival time t:     median = μ ln 2:     σ= 1/λ:

x:

CDF(x)=P[X≤x]= 1-e^-λx:=p = -ln(1-p) / λ = x

Integer values k up to your x.
  k        CDF(k)              delta              pdf(k)