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## A question of conditional probability

I encountered a question about conditional probability in statistics. I want to figure out whether the equation below is true: $$P(x|y_1,y_2,y_3)=P\left[ (x|y_1,y_2) | y_3 \right],$$ where $y_1,y_2,y_3$ are some conditions and $x$ is an event that we concern. That’s meaning that if I could treat $(x|y_1,y_2)$ as a whole event?

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## Handling Uncertainty with Budget Constraints in Robust Optimization

Let’s say I have a linear optimization problem with some uncertain parameters Case 1: Uncertain Parameters are present independently in different constraints $$maximize\ x_1+x_2$$ $$ax_1+bx_2\leq 6$$ $$x_1,x_2\geq 0$$ $$\bar{a}=3, \bar{b}=5$$ where a & b are uncertain parameter $a\in [1.5,4.5 ]$($\pm 1.5$ from mean) and $b\in [3,7 ]$ ($\pm 2$ from mean). I solved this […]