Consider an ideal gas of particles with mass m. the probability that a particle is moving at a speed v is proportional to exp(-mv2kt), where v is the magnitude of the three-dimensional velocity vector. (hint: you can use any coordinate system to do these calculations, but be careful to perform the change of variables properly, including the correct differential element if you use spherical or cylindrical polar coordinates.] (a) determine the normalized probability that a particle is moving with speed v, where v is the magnitude of the three-dimensional velocity vector. (b) determine the average speed of the particles, where the speed v is the magnitude of the three- dimensional velocity vector. (c) determine the average kinetic energy of the particles. (d) determine the average value of vxy, where vx represents the magnitude of the component of the velocity in the x-y plane.