Answer:
F(a) =2a^2+4a+5
Step-by-step explanation:
just put x= a
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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Given: Security Service Company:
1.4 1.8 1.6 1.7 1.5 1.5 1.7 1.6 1.5 1.6
Mean: 1.59
Standard Deviation: 0.014333
Other companies: 1.8 1.9 1.6 1.7 1.6 1.8 1.7 1.5 1.8 1.7
Mean: 1.71
Standard deviation: 0.014333
The coefficient of variation for security Service Company:
CV = (Standard Deviation/Mean) * 100.
= (0.14333/1.59) * 100
= 9.01%
The coefficient of variation for other companies:
CV = (Standard Deviation/Mean) * 100.
= (0.014333 / 1.71) * 100
= 8.38%
the limited data listed here show evidence of stealing by the security service company's employees because there is a significant difference in the variation.
Answer:
The sample mean is
b.3.55
The margin of error is
0.32
Step-by-step explanation:
Deep explanation about a confidence interval
We have that to find our 
level, that is the subtraction of 1 by the confidence interval divided by 2. So:
Now, we have to find z in the Ztable as such z has a pvalue of 
.
So it is z with a pvalue of 
, so 
Now, find M as such
In which 
is the standard deviation of the population and n is the size of the sample.
The lower end of the interval is the mean subtracted by M. So it is 6.4 - 0.3944 = 6.01 hours.
The upper end of the interval is the mean added to M. So it is 6.4 + 0.3944 = 6.74 hours.
In this problem:
The deep explanation is not that important.
We just have to recognize that the interval has a lower end and an upper end. The distance from both the upper and the lower end to the mean is M. This means that the sample mean is the halfway point between the lower end and the upper end.
The margin of error is the distance of these two points(lower and upper end) to the mean.
In our interval
Lower end: 3.23
Upper end: 3.87
Sample mean
So the correct answer is:
b.3.55
The margin of error is
3.87 - 3.55 = 3.55 - 3.23 = 0.32
