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In: Statistics and Probability

The velocity of a particle in a gas is a random variable X with probability distribution...

The velocity of a particle in a gas is a random variable X with probability distribution

fX (x)  =  32 x2 e−4x , x>0. The kinetic energy of the particle is (1/2) mX 2.  Suppose that the mass of the particle is 64 yg. Find the probability distribution of Y. (Do not convert any units.) Please explain steps. I do not understand how to solve this kind of question. Thank you! :)

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Answer:-

Given That:-

The velocity of a particle in a gas is a random variable X with probability distribution
fX (x)  =  32 x2 e−4x , x>0. The kinetic energy of the particle is (1/2) mX 2.  Suppose that the mass of the particle is 64 yg. Find the probability distribution of Y. (Do not convert any units.)

Given,

C.D.F

  

Where   = cdf of X, m = 64 yg, y > 0

pdf probability density function:

Therefore,

  

Thus the probability distribution of Y :

Thank you for your Supporting. Please upvote my answer...

orchestra answered 2 years ago
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