# What is the Probability Density Function of the Binomial Distribution?

Suppose we have the Probability Mass Function (PMF) of the Binomial Distribution here:

$Bin(k|n,\theta) = {n \choose k} \theta^k (1 - \theta)^{n-k}$

How do we derive the Probability Density Function (PDF)? Is that not possible since 'k' in this case is a discrete random variable and not continuous?

• Discrete random variables do not have a density. They do have a cumulative distribution function – Henry Jul 5 '17 at 22:16
• It is common to interpret the PDF as a density w.r.t. the Lebesgue measure. In that context a discrete random variable has no PDF (as @Henry remarks). Nevertheless in the discrete situation the PMF is actually also a density, but this w.r.t. a suitable counting measure. – drhab Jul 6 '17 at 8:03