expected variable
expected value of a die: (1/6)*1 + (1/6)*2 + (1/6)*3 + ... (1/6)*6 = 7/2 expected value with large outcomes
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. Geometric Distribution
If random variable X has the geometric distribution with parameter p, then E(x) = 1/p. (expected value) Expected value IRV
Theorem Variance
Variance => how widely the values of expected value of a random value is distributed. Variance of the number of successes in n Bernoulli trials is npq, where q is 1 - p |
Chebyshev's Inequality
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. Equivalence Relation
If relations a and b are related by an equivalence relation, they are equivalent, denoted by a ~ b Graph Terminology
. Bipartite Rules for Special Simple Graphs
. Strong vs Weak conn.
Strongly connected graph is also weakly connected. Look for strong components (vertices and cycles) |
Euler Circuit Rules for Spec. Graphs
. Euler circuit
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. |
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EECS 203 Final Exam Cheat Sheet Cheat Sheet by Kalbi
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