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### 7.3

Course: MATH 6040, Fall 2008
School: Utah
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Word Count: 115

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If 7.3. X is uniform-[0, 1], then E e If Y is uniform=[b, a + b], then E e itY it(aX+b) = 1 0 e it(ax+b) eit(a+b) - eitb dx = . iat = a+b eity b eit(a+b) - eitb dy = . a iat The uniqueness theorem does the rest. Next suppose Z is uniform-[0, 1]. Then Z = 2-i Zi where the Zi 's i=1 are 1 i.i.d. with values in {0, 1} with probability 2 each. From Problem 1.15 we know that X = 2Z - 1 is uniform[-1, 1]. But...

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If 7.3. X is uniform-[0, 1], then E e If Y is uniform=[b, a + b], then E e itY it(aX+b) = 1 0 e it(ax+b) eit(a+b) - eitb dx = . iat = a+b eity b eit(a+b) - eitb dy = . a iat The uniqueness theorem does the rest. Next suppose Z is uniform-[0, 1]. Then Z = 2-i Zi where the Zi 's i=1 are 1 i.i.d. with values in {0, 1} with probability 2 each. From Problem 1.15 we know that X = 2Z - 1 is uniform[-1, 1]. But X = 2 2Zi - 1 = 2 (2Zi - 1) = 2-i Xi , -...

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