Download Cybersecurity and Applied Mathematics by Leigh Metcalf, William Casey PDF

By Leigh Metcalf, William Casey

Cybersecurity and utilized arithmetic explores the mathematical recommendations useful for potent cybersecurity examine and perform, taking an utilized technique for practitioners and scholars getting into the sector. This e-book covers tools of statistical exploratory info research and visualization as a kind of version for riding judgements, additionally discussing key themes, akin to graph thought, topological complexes, and chronic homology. protecting the net is a posh attempt, yet making use of the proper thoughts from arithmetic could make this job extra possible. This booklet is vital examining for growing beneficial and replicable equipment for examining information.

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Sample text

An discrete random variables and a pmf of f (x), then the expected value of the discrete random variable is given in Eq. 10) It is a weighted average of the random variable and can be thought of as the value we anticipate from the distribution. 1, then the value we will most likely see in our distribution is close to 1, as we see from computing the expected value. 1. 1. We want to have a general idea of about how long this laptop battery will last. 2 From parlor tricks to random variables The answer is the expected value.

This final of the Data Analysis process is called Inference. To summarize, the Data Analysis process starts with a population and the first step is to produce data. This generates data from the population and enables the second step, exploratory data analysis. The third and final step applies probability methods to the data to enable information about the population to be inferred. This is illustrated in Fig. 1. This diagram is a “big picture” and is a good way of thinking about the process. In some situations, we can see exactly and immediately what the data and probability models and inference might be.

Let us digress for a moment into math. If we have another function g(x) and compose f (x) and g(x) as f (g(x)), then we can consider the pdf of f (g(x)). Now we are no longer asking f (x) = P(X ≤ x) but asking f (g(x)) = P(X ≤ g(x)). We can also find the expected value of g(x), which we write as E(g(x)). It can be shown that E(g(x)) = g(x)f (x)dx for a continuous random variable. In the discrete case, it is E(g(x)) = g(x)f (x). ” We could have a random variable that is clustered around the mean with only a few values far from it, or we could have one that is distributed equally far on both sides of the mean, but is not close to it at all.

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