WebUsing Jensen´s inequality to explain the role of regular….pdf. 2024-07-05上传. Using Jensen´s inequality to explain the role of regular… WebJensen’s Inequality is a statement about the relative size of the expectation of a function compared with the function over that expectation (with respect to some random variable). To understand the mechanics, I first define convex functions and then walkthrough the logic behind the inequality itself. 2.1.1 Convex functions
Using Jensen´s inequality to explain the role of regular… - 豆丁网
WebJensen’s Inequality: Let C Rdbe convex and suppose that X2C. Provided that all expectations are well-defined, the following hold. (1)The expectation EX2C (2)If f: C!R is convex then … WebMar 24, 2024 · (1) If f is concave, then the inequality reverses, giving f(sum_(i=1)^np_ix_i)>=sum_(i=1)^np_if(x_i). (2) The special case of equal p_i=1/n with the … hbw 2 10 warranty program
Convexity and Jensen
WebApr 29, 2024 · Jensen's inequality for indefinite integrals. In many sources, for example here, we can find the following generalisation of Jensen's inequality. In real analysis, we may require an estimate on φ ( ∫ a b f ( x) d x), where a, b ∈ R and f: [ a, b] → R is a non-negative Lebesgue-integrable function. In this case, the Lebesgue measure of ... WebTHE JENSEN INEQUALITY. Let f be a function with a positive second derivative. Such a function is called ``convex" and satisfies the inequality. Equation ( 1) relates a function of an average to an average of the function. The average can be weighted, for example, Figure 1 is a graphical interpretation of equation ( 2 ) for the function f = x2. WebFor example, if ’(x) = jxj, then a tangent line for ’at 0 may have any slope between 1 and 1 (see gure 2). We shall use the existence of tangent lines to provide a geometric proof of the ... Theorem 4 Jensen’s Inequality (Integral Version) Let (X; ) be a measure space with (X) = 1. Let ’: (a;b) !R be a convex hbw 35 floating valve automatic