still stuck with the probability concept

hi everyone, i am not a math geek and don't know why the hell i chose thermodynamics this semester with this little math knowledge, but can you please help me figure out the basic difference between discrete and continuous probability?
in thermodynamics we are sometimes taking the probability with summation, sometimes with integration and even sometimes the mean <X> is being zero , we are counting the <X^2> squared mean....

now my question is why are we supposed to find different types of probability and why do we take the squared mean of parameters like gas velocity or number of molecules etc..

plz help out

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 Quote by cooper607 hi everyone, i am not a math geek and don't know why the hell i chose thermodynamics this semester with this little math knowledge, but can you please help me figure out the basic difference between discrete and continuous probability? in thermodynamics we are sometimes taking the probability with summation, sometimes with integration and even sometimes the mean is being zero , we are counting the squared mean.... now my question is why are we supposed to find different types of probability and why do we take the squared mean of parameters like gas velocity or number of molecules etc.. plz help out
Hey cooper607 and welcome to the forums.

It sounds like you are using this to calculate the variance. The variance is one way of describing the spread of a random variable, or a measure of how 'uncertain' a random variable is but this is not the only way to assess uncertainty.

In relation to your example, the definition of VAR[X] = E[X^2] - (E[X])^2. Take a look at this for more information:

http://en.wikipedia.org/wiki/Variance

still stuck with the probability concept

thanks a lot viraltux and chiro.... you guys really helped me at least getting the marginal idea on probability... i am too unfortunate not to switch the thermodynamics course to statistics and that's why i have been asking for help :( :(

anyway it helped me get the hold a little bit....

be prepared for my next silly questions :)

regards for you again .....

 In addition to Chiro's answer-- that the average of squares is related to variance-- let me add that if you are looking at the average of the square velocity of particles in thermodynamics, there is a good chance this is because the square of velocity is proportional to kinetic energy. (Not that I know anything about thermodynamics.)