Consider the probability density function p(%) (a/r)3/2 e ng for the velocity of a particle in the r-direction. the probability densities for vy and v have the same form. each of the three velocity components can range from-to +oo and a is a constant. this form of the probability density for the velocity will be derived in section 6.2.2 for a classical system of particles at temperature t (a) show that p(v) is normalized. use the fact that see (a.15)] (3.123) note that this calculation involves doing three similar integrals that can be evaluated sepa- rately (b) what is the probability that a particle has a velocity between tr and vェ+da, vy and vy +dus and v andv du? (c) what is the probability that t 0, vy 0, u: > 0 simultaneously?