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I have a dataset with 4 features and 150 examples.(150*4 matrix). Now I am confused with two concepts here:

  1. What are random variables in this dataset? Are they each of the 4 individual features? ($X_1$,$X_2$,$X_3$,$X_4$)

  2. If I am sampling 50 examples from this dataset(50*4 matrix), what is meant by the sample mean? Is it a vector of individual means of the random variables $X_1$,...$X_4$ for 50 elements or is it {$X_{1m}$ , $X_{2m}$, $X_{3m}$, $X_{4m}$}.

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1) You say you have 4 features, and 150 examples. In this case, you have 4 variables, and 150 samples (samples ~ examples,realizations). Then indeed, the 4 features $X_1,X_2,X_4,X_4$ are your random variables

2) Sampling 50 examples from the dataset gives you a 50x4 matrix. Then, from this reduced sample, you can compute the moments (mean, variance, etc), and for the mean, it gives you a vector of 4 elements $\bar{X}_1,\bar{X}_2,\bar{X}_3,\bar{X}_4$, where $\bar{X}_i = \frac{1}{50}(X_{i,1} + X_{i,2}+\dots+X_{i,50})$

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