Jensen's inequality expectation proof
2018年12月24日 — Theorem 1 (Jensen's Inequality) Let ϕ be a convex function on R and let X ∈ L1 be integrable. Then. ϕ(E[X]) ≤ E[ϕ(X)]. One proof with a nice ... ,2.1 Jensen's Inequality. Jensen's Inequality is a statement about the relative size of the expectation of a function ... The majority of this proof is straightforward. ,Usually the right hand side above — f of an expectation — is simpler than the left hand side — the expectation of f. Jensen's inequality is used to bound. ,Remember that variance of every random variable X is a positive value, i.e., ... Jensen's inequality states that, for any convex function g, we have E[g(X)]≥g(E[X]) ... ,Jensen's inequality: statement, proof, examples, solved exercises. ... Jensens's inequality concerns the expected value of convex and concave transformations of ... ,Theorem 1. Any convex function f : Rn → R is continuous, and even locally Lipschitz contin- uous. Proof. Step 1: ... ,跳到 Proof 3 (general inequality in a probabilistic setting) — Proofs[edit]. A graphical "proof" of Jensen's inequality for the probabilistic case. The ... ,Proof. Suppose f is differentiable. The function f is concave if, for any x and y, ... This inequality is true for all X, so we can take expectation on both sides to get. ,
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 Jensen's inequality expectation proof 相關參考資料
5 Expectation Inequalities and Lp Spaces
2018年12月24日 — Theorem 1 (Jensen's Inequality) Let ϕ be a convex function on R and let X ∈ L1 be integrable. Then. ϕ(E[X]) ≤ E[ϕ(X)]. One proof with a nice ... https://www2.stat.duke.edu Chapter 2 Inequalities involving expectations | 10 ... - Bookdown
2.1 Jensen's Inequality. Jensen's Inequality is a statement about the relative size of the expectation of a function ... The majority of this proof is straightforward. https://bookdown.org Convexity and Jensen's Inequality
Usually the right hand side above — f of an expectation — is simpler than the left hand side — the expectation of f. Jensen's inequality is used to bound. https://ttic.uchicago.edu Jensen's Inequality
Remember that variance of every random variable X is a positive value, i.e., ... Jensen's inequality states that, for any convex function g, we have E[g(X)]≥g(E[X]) ... https://www.probabilitycourse. Jensen's inequality - Glossary - StatLect
Jensen's inequality: statement, proof, examples, solved exercises. ... Jensens's inequality concerns the expected value of convex and concave transformations of ... https://www.statlect.com Jensen's inequality - UiO
Theorem 1. Any convex function f : Rn → R is continuous, and even locally Lipschitz contin- uous. Proof. Step 1: ... https://www.uio.no Jensen's inequality - Wikipedia
跳到 Proof 3 (general inequality in a probabilistic setting) — Proofs[edit]. A graphical "proof" of Jensen's inequality for the probabilistic case. The ... https://en.wikipedia.org Jensen's Inequality Theorem For any concave function f, E[f(X ...
Proof. Suppose f is differentiable. The function f is concave if, for any x and y, ... This inequality is true for all X, so we can take expectation on both sides to get. http://www.sef.hku.hk Lecture Notes 2 36-705 1 Markov Inequality 2 Chebyshev ...
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