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As with any probability class we started off learning discrete distributions like binomial, Poisson, hypergeometric. We called formulas like $P(X=x)=\begin{pmatrix}n\\x\end{pmatrix}p^x q^{n-x}$ the PMF (loosely PDF) of the binomial distribution. The CDF, I assume, would be like $P(X\leq x)$. However, when moving on to continuous distributions I realized PDFs don't given probability (since probability of a point is zero), and it's CDFs that give a probability.

Then, what is the accurate thing to call the binomial formula above? Given it's discrete, this formula solving for $X=x$ does give a "probability", but we called it a PDF? Aren't PDF's just supposed to be a function mapping to any real number? Can I say the binomial CDF is $P(X\leq x)$ ?

Note: this doesn't affect my understanding of how I used them, but I just want to refer to them in the most accurate way possible, since it gets confusing when we refer to continuous PDFs as $f(x)$ and CDFs as $F(x)$ but these discrete 'pmfs' were $P(x)$

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