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The theory of subjective expected utility combines two concepts: first, a personal utility function, and second, a personal probability distribution (usually based on Bayesian probability theory). This theoretical model has been known for its clear and elegant structure and is considered by some researchers to be "the most brilliant axiomatic ...
An arbitrary function φ : R n → C is the characteristic function of some random variable if and only if φ is positive definite, continuous at the origin, and if φ(0) = 1. Khinchine’s criterion. A complex-valued, absolutely continuous function φ, with φ(0) = 1, is a characteristic function if and only if it admits the representation
A recent large-scale (u = 336,691) analysis of sex differences based on the five moral foundations suggested that women consistently score higher on care, fairness, and purity across 67 cultures. [53] However, loyalty and authority were shown to have negligible sex differences, highly variable across cultures.
The increasing sophistication of justice-based reasoning was taken as a sign of development. Moral cognitive development, in turn, was assumed to be a necessary (but not sufficient) condition for moral action. [34] But researchers using the Kohlberg model found a gap between what people said was most moral and actions they took.
The more special case of the isoelastic utility function, with constant relative risk aversion, occurs if, further, b = 0. The logarithmic utility function occurs for = as goes to 0. The more special case of constant relative risk aversion equal to one — U(W) = log(W) — occurs if, further, b = 0.
An example of normative ethical philosophy is the Golden Rule, which states: "One should treat others as one would like others to treat oneself." [ 3 ] [ 4 ] Immorality is the active opposition to morality (i.e., opposition to that which is good or right), while amorality is variously defined as an unawareness of, indifference toward, or ...
Based on both the von Neumann-Morgenstern and Nash Game Theory model, a risk-averse person will happily receive a smaller commodity share of the bargain. [22] This is because their utility function concaves hence their utility increases at a decreasing rate while their non-risk averse opponents may increase at a constant or increasing rate. [23]
Here, as usual, stands for the conditional expectation of Y given X, which we may recall, is a random variable itself (a function of X, determined up to probability one). As a result, Var ( Y ∣ X ) {\displaystyle \operatorname {Var} (Y\mid X)} itself is a random variable (and is a function of X ).