10. Is it possible for X, Y, and Z to have the same distribution and satisfy X = U(Y + Z), where U is uniform on [0, 1], and Y, Z are independent of U and of one another? (This question arises in modelling energy redistribution among physical particles.)

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10. Is it possible for X, Y, and Z to have the same distribution and satisfy X = U(Y + Z), where
U is uniform on [0, 1], and Y, Z are independent of U and of one another? (This question arises in
modelling energy redistribution among physical particles.)
Transcribed Image Text:10. Is it possible for X, Y, and Z to have the same distribution and satisfy X = U(Y + Z), where U is uniform on [0, 1], and Y, Z are independent of U and of one another? (This question arises in modelling energy redistribution among physical particles.)
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