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Suppose F is a probability distribution with chf (t). Prove for all a > 0 0 1 - cos at (F(x + u) - F(x

Suppose F is a probability distribution with chf (t). Prove for all a > 0
0 1 - cos at (F(x + u) - F(x - u)) du = e ,-itx 12 p(t) dt, - 0o and u 0 1 - cos ax $ (t)dt = 2 F(dx). 0 -u - OO x2

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Question

Suppose F is a probability distribution with chf (t). Prove for all a > 0 0 1 - cos at (F(x + u) - F(x

Suppose F is a probability distribution with chf (t). Prove for all a > 0 0 1 - cos at (F(x + u) - F(x - u)) du = e ,-itx 12 p(t) dt, - 0o and u 0 1 - cos ax $ (t)dt = 2 F(dx). 0 -u - OO x2

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Recommended Textbook for

Income Tax Fundamentals 2013

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Suppose F is a probability distribution with chf (t). Prove for all a > 0
0 1 - cos at (F(x + u) - F(x - u)) du = e ,-itx 12 p(t) dt, - 0o and u 0 1 - cos ax $ (t)dt = 2 F(dx). 0 -u - OO x2