Question
Suppose f and g are non-negative bounded Borel functions. Let X1 and X2 be random variables A. Show that ( f (X1) f (X2))(g(X1) g(X2))
Suppose f and g are non-negative bounded Borel functions. Let X1 and X2 be random variables
A. Show that ( f (X1) f (X2))(g(X1) g(X2)) is a non-negative random variable.
B. Now suppose that X1 andX2 are independent and equi-distributed. Show that 2Cov(f(X1),g(X1)) = Cov( f (X1) f (X2), g(X1) g(X2)).
C. Show that Cov( f (X1), g(X1)) 0.
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Statistical Techniques in Business and Economics
Authors: Douglas A. Lind, William G Marchal
17th edition
1259666360, 978-1259666360
