Answer:
The constant of proportionality is the ratio between numbers that expresses the rate at which the numbers increase or decrease. These two numbers are directly proportional when they increase and decrease at the same rate.
Answer:
The given sides does not form a triangle
Step-by-step explanation:
The given sides does not form a triangle
We know the triangle property which states that the sum of any two sides of the triangle should be greater than the third side.
Here given th esides of the triangle are 6x,7x,21x
6x+7x=13x < 21x
for any value of x the above equation does not satisfy.
C=<span>1 is the answer my good man have a good day :)</span>
Pittsburgh because -9°F is colder than -7<span>°F</span>
Distributionally robust stochastic programs with side information based on trimmings
This is a research paper whose authors are Adrián Esteban-Pérez and Juan M. Morales.
Abstract:
- We look at stochastic programmes that are conditional on some covariate information, where the only knowledge of the possible relationship between the unknown parameters and the covariates is a limited data sample of their joint distribution. We build a data-driven Distributionally Robust Optimization (DRO) framework to hedge the decision against the inherent error in the process of inferring conditional information from limited joint data by leveraging the close relationship between the notion of trimmings of a probability measure and the partial mass transportation problem.
- We demonstrate that our technique is computationally as tractable as the usual (no side information) Wasserstein-metric-based DRO and provides performance guarantees. Furthermore, our DRO framework may be easily applied to data-driven decision-making issues involving tainted samples. Finally, using a single-item newsvendor problem and a portfolio allocation problem with side information, the theoretical findings are presented.
Conclusions:
- We used the relationship between probability reductions and partial mass transit in this study to give a straightforward, yet powerful and creative technique to expand the usual Wasserstein-metric-based DRO to the situation of conditional stochastic programming. In the process of inferring the conditional probability measure of the random parameters from a limited sample drawn from the genuine joint data-generating distribution, our technique generates judgments that are distributionally resilient to uncertainty. In a series of numerical tests based on the single-item newsvendor issue and a portfolio allocation problem, we proved that our strategy achieves much higher out-of-sample performance than several current options. We backed up these actual findings with theoretical analysis, demonstrating that our strategy had appealing performance guarantees.
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