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Difference between pmf and pdf. Watch

1. Hey, can someone please explain to me the difference between the probability mass function and probability density function? They seem like exactly the same thing to me.
2. Well... depends. What level are you studying at? In measure theory, these are the same thing - a p.m.f. is a density with respect to counting measure which induces a probability measure, and a p.d.f. is a density, typically with respect to Lebesgue measure, which induces a probability measure. In more elementary probability theory / statistics, a p.m.f. is something which tells you the probability that a discrete random variable takes a particular value, and a p.d.f. is something you integrate to get the probability that an (absolutely) continuous random variable takes a particular set of values.

Essentially, a p.m.f. is something you sum and a p.d.f. is something you integrate.
3. (Original post by Zhen Lin)
Well... depends. What level are you studying at? In measure theory, these are the same thing - a p.m.f. is a density with respect to counting measure which induces a probability measure, and a p.d.f. is a density, typically with respect to Lebesgue measure, which induces a probability measure. In more elementary probability theory / statistics, a p.m.f. is something which tells you the probability that a discrete random variable takes a particular value, and a p.d.f. is something you integrate to get the probability that an (absolutely) continuous random variable takes a particular set of values.

Essentially, a p.m.f. is something you sum and a p.d.f. is something you integrate.
Thanks, I'm a first year undergraduate so the first part made no sense to me . But I understand the second part. Just a question though, if i put say 0.6 into the pdf then what is that supposed to measure?
4. Nothing in particular. The value the p.d.f. takes at a particular point doesn't matter very much - what does matter is the behaviour of the p.d.f. on a neighbourhood around that point.
5. Thanks!

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