How to find skewness and kurtosis from pdf?

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I am given a data set of velocity($u$) & time ($t$). And Asked to calculate the pdf.

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I have computed the pdf from the given data after coding it on Matlab. And fitted a $10$th order polynomial.

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According to the second problem, I'm supposed to evaluate mean,rms, skewness and kurtosis. So do I have to use this fitted curve of pdf as a function of u and calculate these quantities by integration? As they are defined.

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The above is the method, I've been taught by the professor.