are x and y independent?
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Intuitively, two random variables X and Y are independent if knowing the value of one of them does not change the probabilities for the other one. In other words, if X and Y are independent, we can write P(Y=y|X=x)=P(Y=y), for all x,y.
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If X and Y are independent, then Var(X + Y) = Var(X) + Var(Y) and Var(X - Y) = Var(X) + Var(Y).
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There are many situations when we might wish to know whether a set of vectors is linearly dependent, that is if one of the vectors is some combination of the others. If u and v are linearly independent, then the only solution to this system of equations is the trivial solution, x=y=0.
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Roughly speaking, independent variables represent function inputs, while dependent variables represent function outputs. The value of a dependent variable depends on what the input is.
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So, whatever is your independent quantity, is usually plotted on the horizontal axis, as if it needs no support, like time. And the other quantity that needs support is plotted on (parallel) to the vertical axis. ... Vertical axis (y) against / versus Horizontal axis (x).
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Two events are independent, statistically independent, or stochastically independent if the occurrence of one does not affect the probability of occurrence of the other (equivalently, does not affect the odds).
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So x is usually called the independent or explanatory variable, and y the dependent or response variable. Another way to think about it, sometimes, is that x is used to predict y. So x is something that comes before y in time. That is why, for example, height at age 2 is on the x axis and height at age 18 on the y.
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Choose your x and y carefully. Scientists like to say that the “independent” variable goes on the x-axis (the bottom, horizontal one) and the “dependent” variable goes on the y-axis (the left side, vertical one).
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A set of vectors { v 1 , v 2 ,..., v k } is linearly independent if and only if, for every j , the vector v j is not in Span { v 1 , v 2 ,..., v j − 1 } .
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Independent Events Venn Diagram Theorem: If X and Y are independent events, then the events X and Y' are also independent. Proof: The events A and B are independent, so, P(X ∩ Y) = P(X) P(Y). From the Venn diagram, we see that the events X ∩ Y and X ∩ Y' are mutually exclusive and together they form the event X.
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Are x and y both positive? This just means that x and y have the same sign. They're either both positive or both negative.
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If a consistent system has exactly one solution, it is independent . ... If a consistent system has an infinite number of solutions, it is dependent . When you graph the equations, both equations represent the same line. If a system has no solution, it is said to be inconsistent .
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Independence. Two events A and B are called independent if P(A|B)=P(A), i.e., if conditioning on one does not effect the probability of the other. Since P(A|B)=P(AB)/P(B) by definition, P(A)=P(AB)/P(B) if A and B are independent, hence P(A)P(B)=P(AB); this is sometimes given as the definition of independence.
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Events A and B are independent if: knowing whether A occured does not change the probability of B. Mathematically, can say in two equivalent ways: P(B|A) = P(B) P(A and B) = P(B ∩ A) = P(B) × P(A).
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If the two equations describe parallel lines, and thus lines that do not intersect, the system is independent and inconsistent. If the two equations describe the same line, and thus lines that intersect an infinite number of times, the system is dependent and consistent.
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The dependent variable is usually graphed on the y-axis, and the independent variable is usually graphed on the x-axis. In addition, the value of the independent variable determines the value of the dependent variable and is used in experiments to test the value of the dependent variable.
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So if you are able to isolate one coordinate in an implicit form, this coordinate is called dependent, the other independent. In x=1/y the coordinate x is dependent and y independent whereas in y=1/y it's vice versa.