Still stuck with the probability concept

[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 <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..

please help out

 

[chiro]

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..

please 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

 

[viraltux]

I will add to chiro's answer that you really really need a good basic introductory course in statistics. Is it too late to swap your course in thermodynamics for a course in statistics/probability?

But anyway, answering to your question and making it way simple; discrete would be something you can count with your fingers 0,1,2,3... e.g. the number of people studying thermodynamics. continuous would be something you cannot count with your fingers and you need decimal values e.g. 5.854 hours studying thermodynamics each week.

So, let's say your thermodynamic class have room for only 40 students and that I want to find out information about the number of students that will assist next day to class. Then you could assume that every number 0,1,2,3... to 40 will have a probability P(0), P(1)... P(40) and to add these kind of magnitudes we use summation.

And now let's say you want info about the the hours you will study next week assuming you cannot study more than 40 hours. Then you have from 0 to 40 an infinite amount of values 0.001, ∞, 0.001100, ∞, 0.0011100..., ∞, 39.9999, ∞, 39.999999, ∞, 40, the probabilities for these values will be infinitesimals (something that it is nearly zero) and to add these infinite and nearly zero infinitesimals magnitudes we use integration.

Now, I tried to simplify it as much as I can but, again, you reaaaally need an introductory course to Calculus / Statistics / Probability otherwise you're going to struggle to grasp anything about thermodynamics.

Good Luck Cooper!

 

[cooper607]

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 ...

 

[awkward]

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.)