- #1
squenshl
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Homework Statement
1. According to the Maxwell-Boltzman law of theoretical physics, the probability density of a gas molecule is ##f(v) = kv^2e^{-\beta v^2}## if ##v > 0## and ##f(v) = 0## otherwise, where ##\beta## depends on its mass and absolute temperature, and ##k## is an appropriate constant. Show that the p.d.f. of the kinetic energy ##E##, whose values are related to those of ##V## by means of the equation ##E = \frac{1}{2}mV^2## has a Gamma distribution.
2. Repeat the derivation when ##V \sim N(0,\sigma^2)##.
Homework Equations
The Attempt at a Solution
For 1. I'm not too sure what exactly they are asking. Are they asking for pdf of E and how does that relate to the pdf ##f(v)##?
For 2. I'm sure it just follows on from 1.