November 28, 2024
The binomial distribution is the foundation of almost everything, describing the probability distribution of the number of successes \(k\) in \(n\) independent repeated experiments (Bernoulli trials).
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November 25, 2024
The fundamental property of a matrix is the transformation space, so eigenvalues describe the scaling strength in a certain direction. Eigenvectors describe that direction.
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November 21, 2024
The determinant has nothing to do with “equations”, it is a scalar.
The determinant is only applicable to square matrices, describing the volume of n n-dimensional vectors. For two dimensions, it is the area. A determinant of zero indicates that the matrix cannot span an n-dimensional space, at most n-1 dimensions, i.e., not full rank. So the volume is zero in n dimensions.
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November 12, 2024
This is problem that you may encounter, and I found a simple way to calculate it. The result looks correct after comparing with the actual data. A website receives an average of 1000 requests per hour, and can only handle one at a time, taking 1 second. When a request arrives, if the previous one has not been completed, an error will occur. How many errors will occur on average in an hour?
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March 18, 2024
With a coding scheme where the minimum hamming distance between two valid codewords is m, it can detect r-bit errors at most when
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March 18, 2024
Matrix multiplication has four cases, but essentially they are all vector operations.
November 30, 2023
The variance measures the dispersion of a random variable, which is the expectation of the squared difference between each data point and the expectation.
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