Changes of sign of sums of random variables
... when the x^ are the Rademacher functions. We conjecture, but have not been able to prove, that ( 1 ) remains true, provided the equality sign be changed to < , for all sequences of identically distributed independent symmetric random variables. We have had more success with lower limits: THEOREM 2. ...
... when the x^ are the Rademacher functions. We conjecture, but have not been able to prove, that ( 1 ) remains true, provided the equality sign be changed to < , for all sequences of identically distributed independent symmetric random variables. We have had more success with lower limits: THEOREM 2. ...
Integrals Don`t Have Anything to Do with Discrete Math, Do They?
... The fruit borne by the instantiation of Theorem 3 to the graphs in Examples 1 and 2 (respectively, a solution to Problem 1 and a proof of Proposition 2) might provide e being the inspiration to consider this theorem in yet another instance, this time with H graph(s) in Example 3. This application of ...
... The fruit borne by the instantiation of Theorem 3 to the graphs in Examples 1 and 2 (respectively, a solution to Problem 1 and a proof of Proposition 2) might provide e being the inspiration to consider this theorem in yet another instance, this time with H graph(s) in Example 3. This application of ...
Fundamental theorem of calculus
The fundamental theorem of calculus is a theorem that links the concept of the derivative of a function with the concept of the function's integral.The first part of the theorem, sometimes called the first fundamental theorem of calculus, is that the definite integration of a function is related to its antiderivative, and can be reversed by differentiation. This part of the theorem is also important because it guarantees the existence of antiderivatives for continuous functions.The second part of the theorem, sometimes called the second fundamental theorem of calculus, is that the definite integral of a function can be computed by using any one of its infinitely-many antiderivatives. This part of the theorem has key practical applications because it markedly simplifies the computation of definite integrals.