Distribution of a random variable , pdf vs probability distribution

[cappadonza]

Hey all i struggling to understand, these concepts. would some explain to me the relationship and differences the distribution of a random variable and a probabiltiy distribution.
wikipedia says this about probability distribution "The probability distribution describes the range of possible values that a random variable can attain and the probability that the value of the random variable is within any (measurable) subset of that range."

Now if you have probability mass funtion or density funtion which gives you the probability of a given set. why do we need a probability distribution funtion what does it buy us, it seems like they both giving us the same things

any help would me much appreciated

 

[mathman]

It is possible to have a probability distribution function which is not differentiable, so there will be no density function.