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Suppose the velocity of a gas molecule of mass m is a random variable with pdf f Y (y) = ay 2 e -by^2 ,

Suppose the velocity of a gas molecule of mass m is a random variable with pdf fY(y) = ay2e-by^2, y>=0, where a and b are positive constants depending on the gas. Find the pdf of the kinetic energy, W = 0.5mY^2, of such a molecule.

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