Suppose that X is a continuous rv with pdf f(x) supported on 20. Let F(x) be the cdf. Show that E(X) = *° aƒ (x) dx = √ (1 —– F(x)) dr . 0 Hint: Since x > 0, you can write x = Sdt. Plug this into the definition of the expected value and swap the order of integration (and look at your Vector Calculus notes to confirm that you can swap the order of integration).

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4. Suppose that X is a continuous rv with pdf f(x) supported on r > 0. Let F(x) be the cdf. Show
that
E(X) = zf(2) dz = 1 - F(2).
"(x)) dr .
Hint: Since a > 0, you can write x =
and swap the order of integration (and look at your Vector Calculus notes to confirm that you can
swap the order of integration).
Ső dt. Plug this into the definition of the expected value
Transcribed Image Text:4. Suppose that X is a continuous rv with pdf f(x) supported on r > 0. Let F(x) be the cdf. Show that E(X) = zf(2) dz = 1 - F(2). "(x)) dr . Hint: Since a > 0, you can write x = and swap the order of integration (and look at your Vector Calculus notes to confirm that you can swap the order of integration). Ső dt. Plug this into the definition of the expected value
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