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college, validate it on sub-sets of the 1000 students that were not included when creating the prediction model, and then use the model to make predictions about new students.

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Day-count Convention / Year Fraction: We denote by )τt( , T the chosen time measure between t and T, which is usually referred as the year fraction between t and T. When t and T are less than one day, )τt( , T is to be interpreted as T – t (in years).

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POL571 Lecture Notes: Expectation and Functions of Random ...

8. Cauchy distribution. A Cauchy random variable takes a value in (−∞,∞) with the fol-lowing symmetric and bell-shaped density function. f(x) = 1 π[1+(x−µ)2]. The expectation of Bernoulli random variable implies that since an indicator function of a random variable is a Bernoulli random variable, its expectation equals the probability.

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model (i.e., a random variable and its distribution) to describe the data generating process. What we observe, then, is a particular realization (or a set of realizations) of this random variable. The goal of statistical inference is to figure out the true probability model given the data you have.

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Random variable Xis continuous if probability density function (pdf) fis continuous at all but a nite number of points and possesses the following properties: f(x) 0, for all x, R 1 1 f(x) dx= 1, P(a<X b) = R b a f(x) dx The (cumulative) distribution function (cdf) for random variable Xis F(x) = P(X x) = Z x 1 f(t) dt; and has properties lim x ...

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