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In mathematics, a quadratic equation (from Latin quadratus 'square') is an equation that can be rearranged in standard form as [1] + + =, where the variable x represents an unknown number, and a, b, and c represent known numbers, where a ≠ 0. (If a = 0 and b ≠ 0 then the equation is linear, not quadratic
The roots of the quadratic function y = 1 / 2 x 2 − 3x + 5 / 2 are the places where the graph intersects the x-axis, the values x = 1 and x = 5. They can be found via the quadratic formula. In elementary algebra, the quadratic formula is a closed-form expression describing the solutions of a quadratic equation.
Formally, an exchangeable sequence of random variables is a finite or infinite sequence X 1, X 2, X 3, ... of random variables such that for any finite permutation σ of the indices 1, 2, 3, ..., (the permutation acts on only finitely many indices, with the rest fixed), the joint probability distribution of the permuted sequence
Moreover, the final row and the final column give the marginal probability distribution for A and the marginal probability distribution for B respectively. For example, for A the first of these cells gives the sum of the probabilities for A being red, regardless of which possibility for B in the column above the cell occurs, as 2 / 3 .
If b ≠ 0, the line is the graph of the function of x that has been defined in the preceding section. If b = 0 , the line is a vertical line (that is a line parallel to the y -axis) of equation x = − c a , {\displaystyle x=-{\frac {c}{a}},} which is not the graph of a function of x .
Then if the random variables X i indicate the number of times outcome number i is observed over the n trials, the vector X = (X 1, ..., X k) follows a multinomial distribution with parameters n and p, where p = (p 1, ..., p k). While the trials are independent, their outcomes X i are dependent because they must sum to n.
The following circuit returns true when at least some of its inputs are true, but not more than two at a time. It implements the equation y = x1 · x2 + x1 · x2 + x2 · x3. A variable is introduced for each gate's output; here each is marked in red: Notice that the output of the inverter with x 2 as an input has two variables introduced. While ...
In probability theory, the expected value (also called expectation, expectancy, expectation operator, mathematical expectation, mean, expectation value, or first moment) is a generalization of the weighted average.