(a) Let d > 0, and let X be a continuous random variable satisfying X ~ øx (t). Make sure to write your answer in terms of real and imaginary parts. Unif[-d, d]. Calculate (b) Let c, d > 0. Use the Inversion Theorem to prove that sin(ct) sin(dt) dt = T min{c, d}. t2 (Hint: this is related to part (a).)

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4. (a) Let d > 0, and let X be a continuous random variable satisfying X~
øx (t). Make sure to write your answer in terms of real and imaginary parts.
Unif[-d, d]. Calculate
(b) Let c, d > 0. Use the Inversion Theorem to prove that
sin(ct) sin(dt)
dt
T min{c, d}.
t2
(Hint: this is related to part (a).)
Transcribed Image Text:4. (a) Let d > 0, and let X be a continuous random variable satisfying X~ øx (t). Make sure to write your answer in terms of real and imaginary parts. Unif[-d, d]. Calculate (b) Let c, d > 0. Use the Inversion Theorem to prove that sin(ct) sin(dt) dt T min{c, d}. t2 (Hint: this is related to part (a).)
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