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    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.
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    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.
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    (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?
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    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.
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    Thanks!
 
 
 
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