Sharp estimate on the supremum of a class of sums of small i.i.d.
... with the estimate of Theorem 1 in this example. We shall apply Theorem 1 for the class of functions F consisting of the indicator functions of all subsets containing at most L points of a set X. To apply Theorem 1 I show that the above defined F is a class of functions with polynomially increasing c ...
... with the estimate of Theorem 1 in this example. We shall apply Theorem 1 for the class of functions F consisting of the indicator functions of all subsets containing at most L points of a set X. To apply Theorem 1 I show that the above defined F is a class of functions with polynomially increasing c ...
This phenomenon of primitive threes of Pythagoras owes it`s
... PACS numbers: 02.10.Ab , 02.30.Xx In book " The last theorem of P.Fermat" by G. Edwards» ,translated from English into Russia and published by "Mir" publishing House in 1980 in Moscow, we read on page 14 (see also [2] ) : «Written in Latin language article by Fermat says that “from the other hand it ...
... PACS numbers: 02.10.Ab , 02.30.Xx In book " The last theorem of P.Fermat" by G. Edwards» ,translated from English into Russia and published by "Mir" publishing House in 1980 in Moscow, we read on page 14 (see also [2] ) : «Written in Latin language article by Fermat says that “from the other hand it ...
Honors Geometry Lesson 2-1: Use Inductive Reasoning
... To show that a conjecture is true, you must show that it is true for _______ cases. ...
... To show that a conjecture is true, you must show that it is true for _______ cases. ...
Solutions - Rounding and Number
... of the number. Rounding is the process for anyone who doesn't care to be exact. That's okay to a point because there are many different uses for numbers. Generally, the size of the number and its use dictates the place to which it should be rounded. For example, the value for the number (pi) given b ...
... of the number. Rounding is the process for anyone who doesn't care to be exact. That's okay to a point because there are many different uses for numbers. Generally, the size of the number and its use dictates the place to which it should be rounded. For example, the value for the number (pi) given b ...
Chapter 3 Finite and infinite sets
... A matching between two sets A and B is a correspondence between them that matches each element of A to just one element of B, and each element of B to just one element of A. (This is not a precise definition; we will see the definition later. But the idea is clear without worrying about how the defi ...
... A matching between two sets A and B is a correspondence between them that matches each element of A to just one element of B, and each element of B to just one element of A. (This is not a precise definition; we will see the definition later. But the idea is clear without worrying about how the defi ...
Law of large numbers
In probability theory, the law of large numbers (LLN) is a theorem that describes the result of performing the same experiment a large number of times. According to the law, the average of the results obtained from a large number of trials should be close to the expected value, and will tend to become closer as more trials are performed.The LLN is important because it ""guarantees"" stable long-term results for the averages of some random events. For example, while a casino may lose money in a single spin of the roulette wheel, its earnings will tend towards a predictable percentage over a large number of spins. Any winning streak by a player will eventually be overcome by the parameters of the game. It is important to remember that the LLN only applies (as the name indicates) when a large number of observations are considered. There is no principle that a small number of observations will coincide with the expected value or that a streak of one value will immediately be ""balanced"" by the others (see the gambler's fallacy)