The discussion focuses on finding the probabilities and cumulative distribution function (CDF) for a Poisson distribution given the condition that p(x=1) equals p(x=2). It is established that this condition leads to specific values for the parameter λ, namely λ = 0 and λ = 2. Participants express confusion about calculating the CDF, F(x), for the Poisson distribution and clarify that F(x) typically represents the cumulative distribution function, defined as P{X ≤ x}. The conversation emphasizes that for discrete distributions like the Poisson, F(x) is computed using a summation involving the probability mass function and the Heaviside Step Function. Overall, the thread highlights the complexities involved in determining the CDF for discrete random variables.