Let g(x) be a function so that the following covariance and expectations are finite numbers. Show...

Let g(x) be a function so that the following covariance and expectations are finite numbers. Show that

cov [g(U), g(1 − U)] = (1/2) E {[g(U1) − g(U2)][g(1 − U1) − g(1 − U2)]} ,

where U ∼ U(0, 1), U1 and U2 are iid U(0, 1). Note you need the fact about the independences of U1 & 1 − U2 as well as 1 − U1 & U2 to show the above identity.

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orchestra answered 2 years ago

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