![]() For example, using the figure, we conclude that if a sequence of random variables converges in probability to a random variable $X$, then the sequence converges in distribution to $X$ as well.įig.7. In this figure, the stronger types of convergence are on top and, as we move to the bottom, the convergence becomes weaker. There are several types of sequences in math such as arithmetic sequences, quadratic sequences, geometric sequences, triangular sequences, square number. Some of these convergence types are ''stronger'' than others and some are ''weaker.''īy this, we mean the following: If Type A convergence is stronger than Type B convergence, it means that Type A convergence implies Type B convergence.įigure 7.4 summarizes how these types of convergence are related. Types of Number Sequences Growing Sequence As the name suggests, the growing sequence is the number pattern where the numbers are present in an increasing. Sequences are a special type in the language and can be thought of as a collection of elements, similar to an array. A sequence might converge in one sense but not another. There are mainly four types of sequences in Arithmetic, Arithmetic Sequence, Geometric Sequence, Harmonic Sequence, and Fibonacci Sequence. Consider the following sequences: a, a +. These are all different kinds of convergence. The sequence in which the successive terms maintain a constant difference is known as an arithmetic progression. There are four types of convergence that we will discuss in this section: ![]() Demonstrate the common interface that can be used to inspect. This sequence might ''converge'' to a random variable $X$. Sequence Types Introduce tuples, the last built-in sequence type that we have yet to encounter. Here, we would like to provide definitions of different types of convergence and discuss how they are related.Ĭonsider a sequence of random variables $X_1$, $X_2$, $X_3$, $\cdots$, i.e, $\big\$.
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