Question

The velocity of a particle in a gas is a random variable X with probability distribution fx(x) = 27x2e-3x x >0. The kinetic energy of the particle is Y = mx?. Suppose that the mass of the particle is 64 yg. Find the probability distribution of Y. (Do not convert any units.)

Answer 1

Answer:- Given that fx(x) = 27 22 e 3x , x>0 Y = ² mx² x= velocity of the particle Where masscm )= 64 kg Now, y = 1 / 2 my? qe dx = t n dy an ang mm [.: x-f] so by transformation are have fyly) - fyla) lett - 21 (Eng)-3%) (max) Scanned with CamScanner

putting m=64 He get a fyly) = 27 (22) 2-3)*4 Suray ✓ 64 = 34 e 3szy sy seves y lee say yoo So, he quied pdf of Y= kinetic energy fylg)= { 32 y e-buy , yoo o co otherwise Scanned with CamScanner