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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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Lecture 6: Discrete Random Variables 19 September 2005 1 Expectation The expectation of a random variable is its average value, with weights in the average given by the probability distribution E[X] = X x Pr(X = x)x If c is a constant, E[c] = c. If a and b are constants, E[aX +b] = aE[X]+b. If X ≥ Y, then E[X] ≥ E[Y] Now let’s think about ...

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2.6 Some common random variables Discrete random variables X˘Bernoulli(p) (where 0 p 1): one if a coin with heads probability pcomes up heads, zero otherwise. p(x) = ˆ p if p= 1 1 p if p= 0 X˘Binomial(n;p) (where 0 p 1): the number of heads in nindependent flips of a coin with heads probability p. p(x) = n x px(1 p)n x X˘Geometric(p ...

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