Which statement best defines the Poisson distribution and its parameter lambda?

A model for repeated independent trials with two outcomes where lambda is the probability of success on a single trial across a fixed number of trials.

A discrete uniform model where lambda is the median count of occurrences per interval and indicates symmetry of the distribution around that count.

A probability model for counts of occurrences in a fixed interval where lambda is the average number of occurrences in that interval.

A continuous distribution for measuring time between events where lambda denotes the variance of the interarrival times across a continuous timeline and controls the spread of the distribution.