After studying about the beta distribution I understood that the beta density function is used to find the densities for the probabilities. Densities may range from 0 to inf. That is if the density of any probability value is more we can say that the probability value is most likely to occur. But when coming to CDF of the beta distribution function, its output is also a probability. If the input and output both are probabilities, what should I understand? "The probability of the occurrence of the probability is say some 0.8?" This is what I understood. Is this correct? What should I do to find the probabilities (not cumulative probabilities) rather than the densities using beta distribution?
I am using beta distribution in Bayesian networks as prior my posterior for each node is defined as
betapdf(X+success, Y+failure) whose output is density not the probability. Now I need to find the joint probability for the network. How can I do that? For extra information see this link: how to find the joint probability for a Bayesian network?