Aparticle’s velocity (in m/s) in a gas is a random variable (let it be v ) with pdf fv (v) = av2 e −bv, v > 0, where b is a constant that depends on the temperature of the gas and the mass of the particle. answer the following questions. (a) what should a be for this to be a valid pdf as a function of b? (b) what is the probability the velocity of the particle is between 10 and 100 meters per second? (c) the kinetic energy of a particle is w = 1 2mv 2 , where v is the speed. what is the pdf of w? (d) what is the mean kinetic energy of a particle as a function of constant b?
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Aparticle’s velocity (in m/s) in a gas is a random variable (let it be v ) with pdf fv (v) = av2 e −...
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