I have a question regarding basic statistics, and while it might seem
foolish to some of you, I would greatly appreciate any help:
Suppose a variable can assume two values, success ( 1, probability p ) or
failure ( 0, probability 1-p ). If n trials are independent and the
probability of success remains the same for each trial, then obviously the
count of successes in n trials is binomial with E(Y)=np and V(Y)=np(1-p).
What I do not understand, and perhaps this doesn't make any sense, but, what
distribution does the original binary variable have? Here, we don't consider
just the count of successes, but rather, the variable with two values.
Obviously, you can derive that the original binary variable has mean p and
variance p(1-p). But does it make any sense to say that it has a
distribution? I understand that this may seem like a dumb question, but for
some reason it is really bothering me. Any help would be greatly
appreciated.
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