Solving Maxwell Boltzmann Random Number Problem

[jenny777]

Hello,

i was given 100 x,y random numbers, and was asked to find:

Using vmin = 0, 5 *vmax as bounds on the x-axis, and P(0) = 0, P(vmax) as bounds on
the y-axis, generate a set of velocities vi where i = 1,...,n producing a set of random numbers from a distribution function. (When such a distribution function has been integrated so that its integral over all values is 1, it is called a it probability density.) Provide a table with the derived velocities, vi. Describe your procedure by working through the first x, y pair explicitly.

So, in order to generate random numbers, i generated dummy variables,
x=0.001~5, increasing by 0.001; so 5000 x values
Then I multiplied my V_max by the x values and called it a V vector.
for y values, I used the maxwell Boltzmann formula to find the probability density P(v).

Now, what am I suppose to do with the given 100 x,y sets? I'm really confused...

Any help will be greatly appreciated

Thank you!

 

[jenny777]

After finding the values, I'm asked to

Plot a graph of P(v) versus v for the above region, connecting values of the probability
density with a smooth curve. Also plot your uniformly-distributed x, y pairs. What fraction
of these pairs fall under the curve?