Thread: Maxwell-Boltzmann law-urgent

According to the Maxwell-Boltzmann law of theoretical physics, the probability density of V, the velocity of a gas molecule, is
f(v)=kv^2*e^(- βv^2), for v>0; =0, elsewhere.
Where β depends on its mass and the absolute temperature and k is an appropriate constant. Show that the kinetic energy E=(1/2)mV^2, where m the mass of the molecule is a random variable having a gamma distribution.

Originally Posted by Yan

According to the Maxwell-Boltzmann law of theoretical physics, the probability density of V, the velocity of a gas molecule, is
f(v)=kv^2*e^(- βv^2), for v>0; =0, elsewhere.
Where β depends on its mass and the absolute temperature and k is an appropriate constant. Show that the kinetic energy E=(1/2)mV^2, where m the mass of the molecule is a random variable having a gamma distribution.

Follow the method shown in this thread: http://www.mathhelpforum.com/math-he...functions.html

If you still have trouble after reading this, please show your working and where you get stuck.

Originally Posted by mr fantastic

Follow the method shown in this thread: http://www.mathhelpforum.com/math-he...functions.html

If you still have trouble after reading this, please show your working and where you get stuck.

The problem is i don't understand what is the question ask for..
can you explain to me? and step by step???

Originally Posted by mr fantastic

Follow the method shown in this thread: http://www.mathhelpforum.com/math-he...functions.html

If you still have trouble after reading this, please show your working and where you get stuck.

In this problem, i'm confuse about the sentence<where m the mass of the molecule is a random variable having a gamma distribution.>what is the relationship between this sentence and the problem?

Originally Posted by Yan

The problem is i don't understand what is the question ask for..
can you explain to me? and step by step???

You're given the pdf for V and asked to find the pdf of .

Now read the thread I gave. If you still have trouble after reading it, please show your working and where you get stuck.

Originally Posted by mr fantastic

You're given the pdf for V and asked to find the pdf of .

Now read the thread I gave. If you still have trouble after reading it, please show your working and where you get stuck.

G(y) = P (Y<y)
= P ( <y)
= 2 P(V< )
= 2* ....

I just confuse about the m, because in the problem, it says that m is a random variable having a gamma distribution. what is this information use for???

Originally Posted by Yan

G(y) = P (Y<y)
= P ( <y)
= 2 P(V< )
= 2* ....

I just confuse about the m, because in the problem, it says that m is a random variable having a gamma distribution. what is this information use for???

There is a comma missing after molecule, it should read:

"Show that the kinetic energy E=(1/2)mV^2, where m the mass of the molecule, is a random variable having a gamma distribution."

m is not a random variable, E (the kinetic energy) is the random variable in question.

CB