Question: 6.2 Let Y be a random variable with a density function given by f(y) = (3/2)y^2, ?1 ? y ? 1, 0, elsewhere. a Find

6.2 Let Y be a random variable with a density function given by f(y) = (3/2)y^2, ?1 ? y ? 1,

0, elsewhere.

a Find the density function of U1 = 3Y .

b Find the density function of U2 = 3 ? Y .

c Find the density function of U3 = Y 2.

The Weibull density function is given by f (y) = (1/?)*m*y^(m?1)*e^(?y^(m /?)), y > 0,

0, elsewhere,

where ? and m are positive constants. This density function is often used as a model for the lengths of life of physical systems. Suppose Y has the Weibull density just given. Find

a the density function of U = Y^m.

b E(Y^k) for any positive integer k.

6.2 Let Y be a random variable with a density function given

by f(y) = (3/2)y^2, ?1 ? y ? 1, 0, elsewhere. a

\f\f

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