In GATE Civil Engineering, when random variables X and Y follow normal distribution, linear transformations (scaling, sum, and difference) preserve the normal distribution, while product, ratio, and square operations do not result in normal distribution.
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Normal Distribution Operations | GATE Civil Engineering #shorts追加:
From engineering measurements to data science, normal distribution is everywhere. Normal distribution is used to analyze the real-world uncertainties in total demand, total measurements, and signal noising. If X and Y follow normal distribution, and X and Y are random variables, in the prospect of GATE previous year question, which operation results also in normal distribution? So, as part of this, if you perform linear transformation, scaling, sum, and difference, if X and Y are random variables, then the resultant will be also a normal distribution. And remember the class, X and Y are random variables following normal distribution. Now, which operations don't fall under normal distribution, even if X and Y are random variables and follow normal distribution, are the first important property is product operation, and also the ratio operation, and the square operation. These three operations, the resultant will not fall as normal distribution. I hope this video will help you.
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