9. Assume the pdf of a continuous r.v. X is a even function, and its cdf is F(x). Prove that for any real number a > 0, we have a) F(-a)= 1- F(a) = 0.5 - f p(x) dx; b) P(|X|

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9. Assume the pdf of a continuous r.v. X is a even function, and its cdf is F(x).
Prove that for any real number a > 0, we have
a) F(-a)= 1- F(a) = 0.5 - f p(x) dx;
b) P(|X| <a) = 2F(a) — 1;
=
Transcribed Image Text:9. Assume the pdf of a continuous r.v. X is a even function, and its cdf is F(x). Prove that for any real number a > 0, we have a) F(-a)= 1- F(a) = 0.5 - f p(x) dx; b) P(|X| <a) = 2F(a) — 1; =
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