Can P(X=Y) be computed where X has an continuous distribution and Y has an discrete distribution? Please explain with the help of an example. Also mention the conditions in which P(X=Y) can be found. In an example where both X and Y are discrete distributions we just need to multiply and add up both the distributions? Please correct me if I am wrong.
The short answer is no, because the probability that a continuous variable is equal to a particular value is always zero. What you can compute is the distribution function, ie \(P(X \leq k, Y \leq k) \). When the distributions are both discrete and independent, yes, you can just add up the multiplied probabilities, taking care to get all the combinations right.
