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) = [" ={(e) dz = (1 - F(2) d . zf(x) dz = Hint: Since z > 0, you can write z = dt. 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).
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) = [" ={(e) dz = (1 - F(2) d . zf(x) dz = Hint: Since z > 0, you can write z = dt. 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).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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) = af(e) da = (1 – F(2)) da .
5 dt. Plug this into the definition of the expected value
Hint: Since a > 0, you can write =
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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