The discussion centers on the probability of two independent events occurring simultaneously, particularly in the context of probability density functions (PDFs) for continuous and discrete distributions. Participants explore the implications of independence and the nature of the distributions involved.
Participants express disagreement regarding the treatment of continuous distributions and the probability of simultaneous occurrences, with multiple competing views presented without a clear consensus.
The discussion highlights the complexity of defining simultaneous occurrences in the context of continuous versus discrete distributions, as well as the need for clarity on independence and dependence in probability calculations.
oneamp said:Hello. I have two probability density functions for two events. I would like to find the probability that they both will occur at the same time. It is simply multiplying the results of the two integrals over the time, correct?
Thank you
That's not true at all. Suppose ##X## and ##Y## are independent normally distributed random variables. Let ##A## be the event that ##X > 0## and ##B## be the event that ##Y > 0##. Clearly the probability of ##A \cap B## is nonzero.mathman said:No. Two events can occur at the same time only if they have discrete distributions. When both have continuous distributions (and are independent) the probability of happening at the same time is 0.
jbunniii said:That's not true at all. Suppose ##X## and ##Y## are independent normally distributed random variables. Let ##A## be the event that ##X > 0## and ##B## be the event that ##Y > 0##. Clearly the probability of ##A \cap B## is nonzero.