# Question: According to the Maxwell Boltzmann law of theoretical physics the probability

According to the Maxwell-Boltzmann law of theoretical physics, the probability density of V, the velocity of a gas molecule, is

Where β depends on its mass and the absolute temperature and k is an appropriate constant. Show that the kinetic energy E = 1/2 mV2, where m the mass of the molecule is a random variable having a gamma distribution.

Where β depends on its mass and the absolute temperature and k is an appropriate constant. Show that the kinetic energy E = 1/2 mV2, where m the mass of the molecule is a random variable having a gamma distribution.

**View Solution:**## Answer to relevant Questions

With reference to Exercise 3.100 on page 107, find the probability density of the distance between the point of impact and the center of the target. A lawyer has an unlisted number on which she receives on the average 2.1 calls every half– hour and a listed number on which she receives on the average 10.9 calls every half– hour. If it can be assumed that the numbers ...If the number of minutes that a doctor spends with a patient is a random variable having an exponential distribution with the parameter θ = 9, what are the probabilities that it will take the doctor at least 20 minutes to ...Use the corollary of Theorem 4.15 on page 136 to show that if X1, X2, . . . , Xn constitute a random sample from an infinite population, then cov(Xr – , ) = 0 for r = 1, 2, . . . , n. Theorem 4.15 If the random variables ...Use Theorem 4.14 on page 135 and its corollary to show that if X11, X12, . . . , X1n1 , X21, X22, . . . , X2n2 are independent random variables, with the first n1 constituting a random sample from an infinite population with ...Post your question