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Suppose one throws a coin 100 times, and gets exactly 50 heads. This is precisely the expected number of heads on average. Nevertheless, if one calculates the probability of 50 successes out of 100 trials, with 0.5 being the probability of success, the probability is : (100 over 50) * 0.5^50*...

Is the set equation required for PMF definition?

If so, I have a follow up question : in the article on Random Variables and Probability Distributions in Britannica, it says What about the 3d axiom of Kolmogorov? If if A and B are mutually exclusive then : P(A union B) = P(A) + P(B) I have seen the same omission in a Coursera course I am...

I am trying to understand what is the relationship between the concept of a probability mass function, and that of a probability measure. It seems to me that a probability mass function is simply a probability measure applied to a discrete random variable. Is that about right?

The following question was posed to me : A person wants to compare between 2 versions of algorithms. He knows he has 100 False Negatives and wants the algorithms to find them. version 1 found 40 out of 100 False Negatives. version 2 found 90 out of 100 False Negatives. Is ver2 better?

I think I understood my mistake. While I have written that The first point is wrong - in standard diff-in-diff estimation, I have learned that one is supposed to calculate difference-in-difference between averages before, and averages after. I simply missed that. Thanks.

Hello, Difference in difference estimation implies calculating (P2-P1)-(S2-S1). That would give the result of the treatment. It seems to me that the estimation is valid for a specific time point, time 2 at this example. I have read however (for example, at wikipedia), that DiD estimation can...