EECS 203 Final Exam Cheat Sheet Cheat Sheet by Kalbi

expected value of a die: (1/6)*1 + (1/6)*2 + (1/6)*3 + ... (1/6)*6 = 7/2

The expected number of successes when n mutually indepe­ndent Bernoulli trials are performed, where p is the probab­ility of success on each trial, is np.

If random variable X has the geometric distri­bution with parameter p, then E(x) = 1/p. (expected value)

The likelihood that a random variable takes a value far from it's expected value. This inequality provides an upper bound on the probab­ility that the value of a random variable differs from the expected value of the random variable by more than a specified amount.

If relations a and b are related by an equiva­lence relation, they are equiva­lent, denoted by a ~ b

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A connected multigraph with at least two vertices has an Euler circuit if and only if each of its vertices has even degree. It has an Euler path but not a circuit if and only if it has exactly two vertices of odd degree.