What is Random Variable Sequence 10

It is a collection of random variables in a number of columns, and sometimes different theorems require that each random variable have an independent and co-distributed relationship. A random variable sequence is distinguished from a random variable with several value samples.

I feel that random variables are just mappings from some sample space to r, and the reason why they are sequences is because there are a lot of mappings.

The donkey's head on the first floor is not the horse's mouth.

Random variable: A variable that represents a random phenomenon (under certain conditions, a phenomenon that does not always have the same result is called a random phenomenon) and a variable (all possible sample points) of various outcomes. For example, the number of passengers waiting at a bus stop at a given time, the number of calls received by the exchange station in a certain time, and so on, are examples of random variables.

The whole of the possible outcomes of a randomized trial (called the basic events) makes up a basic space. The random variable x is a function defined as a real number in the fundamental space, i.e., every point in the fundamental space, that is, every elementary event has a point on the real axis corresponding to it. For example, if a coin is tossed randomly, there are two possible outcomes: heads up and tails, if x is defined as the number of heads up when a coin is tossed, then x is a random variable, and when heads are up, x takes the value of 1; When the reverse side is facing up, x takes the value of 0.

For example, if x is defined as the number of points that occur when rolling a dice, x is a random variable, and when 1, 2, 3, 4, 5, and 6 occurs, x takes 1, 2, 3, 4, 5, and 6 respectively.

To fully understand a random variable, it is necessary to know not only what values it takes, but also the rules by which it takes these values, that is, to grasp its probability distribution. Probability distributions can be characterized by distribution functions. If you know the distribution function of a random variable, you can find any value it takes and the probability that it falls within a certain value range.

Some random phenomena need to be described by multiple random variables at the same time. For example, the location of the bullet impact point requires two coordinates to determine, and it is a two-dimensional random variable. Similarly, in a random phenomenon that requires n random variables to describe, these n random variables form an n-dimensional random vector.

Describe the value law of random vectors, using a joint distribution function. The distribution function of each random variable in a random vector is called the edge distribution function. If the joint distribution function is equal to the product of the edge distribution function, then these individual random variables are said to be independent of each other.

Independence is an important concept unique to probability theory.

Summary. The randomness of a random sequence is determined by the seed of a random number generator. The seed is a number, it is the starting point of the random number generator, and each random number generated is based on this seed, if the seed does not change, then the generated random number sequence will not change.

The randomness of a random sequence is determined by the seed of the random number generator. The seed is a number, it is the starting point of the random number generator, and each random number generated is based on this seed, if the seed does not change, then the generated random coarse number sequence will not change.

I'm still a little confused, can you be more detailed?

The randomness of a random sequence is mainly determined by a random number generator (RNG). RNG is an algorithm that starts from a specific starting state and generates a series of random numbers with certain rules. If the RNG algorithm is not complex enough, or the starting state of the RNG is not random enough, then the generated random sequence will be repeated, which is called "pseudo-random".

The solution to this problem is to use a more complex RNG algorithm broadband, or to use a more random starting state. Alternatively, more sophisticated algorithms can be used to detect duplications and regenerate random sequences. Personal Tips:

When using random sequences, make sure that both the algorithm and the starting state of the RNG are complex enough to ensure that the generated random sequence is a true random sequence.

Let's just use the example of a coin toss.

Suppose you only use the same coin, assuming that the probability of heads is p, then you flip a coin heads or tails, which is random.

We construct a random variable xn = number of positive occurrences of the number of coins nNote that n refers to the total number of coin drops.

xn is obviously a random variable for any given n.

And then, if n goes from 1 to n, it's a random variable sequence.

Then, from x1 to xn, each element in the sequence of random variables is a random variable.

Then, when the positive integer n tends to infinity, we say that xn converges to x, which can be a random variable or a real number.

In our case, x is a real number, i.e., p

My understanding is that a random sequence is a series of random numbers and random processes that are "ordered and numbered".

is the discipline that studies their statistical properties (especially the "time correlation" property, which is a random variable.

not in the study). Random sequences are generally not labeled (discrete labels, e.g., x1, x2,..It's just that there's a timeline.

Successive designators, e.g. s(t) where t is time), the most important feature is that it is "sequential"!

Unlike normal random variables, where your observational measurement is just a number, for a random sequence, your observational measurement is at least a long list of random numbers.

Here are two examples:

1) The daily price of a certain branch.

Just look at the ** price! This is a typical discrete timeline random sequence with 1-day intervals.

It is affected by many factors, so it is random, but there is still a statistical pattern to follow.

2) The noise curve of the electronic instrument, which is a typical continuous timeline random sequence, you can know the value read from the instrument at any time, the value is random, but this value has statistical rules, such as parameters such as fluctuation range.

The importance of stochastic processes is to study some statistical properties of random sequences, especially the "time correlation" property. For example, finance.

, people have built a large number of models to study the statistical characteristics of the trend, and even use it for stock prices, successful models can help people make large profits.

For example, the ARMA model is taught in finance.

You can look at the references), and made the following assumptions: today's **** price will be affected by the income of the first few days of rent collapse (linear relationship), and a white noise function is added. This is where the important "time-correlative" property of random sequences comes into play.

This is just a simple example.

Stochastic processes play a very important role in engineering, finance, economics and other disciplines, so try to learn it well.

In short, random variables.

A sequence is a list of random variables arranged in some regular order.

Such rules are arbitrary, but emphasize one order.

For example. If xi denotes the result of the ith coin toss, then this sequence is the result sequence of several coin tosses, x1 is the result of the first toss, and xn is the result of the nth toss.

If yi represents the number of times the first i coins tossed heads upwards (the ith face up is xi=1, and the reverse side up is xi=0) then there can be yi=x1+x2+....+xi。In this way, this sequence is a summary sequence of the first i coin tosses, y1 refers to the number of heads of a coin toss, and yn refers to the number of heads of the nth coin tosses.

The random variables in visible are independent of each other, while the random variables in are related to each other, where the outcome of the former affects the latter.

Thus, a random variable sequence is a list of random variables arranged in some regular order.

The statistician used SAS software to generate random sequences by using the random method of random area regression group and stochastic method of leakage and regression".

A third-party statistician uses SPSS statistical software to generate a random scheme using the random number table method"

The discussion of the probability distribution of continuous random variables is discussed in a certain interval, and the probability at any fixed point is zero.

The density function describes the density of a continuous random variable around a certain point.

For example, the English test score obeys a normal distribution with a mean value of 85, and the density function of the normal distribution is taken as the maximum value at 85, which means that the test takers with a score around 85 have the most.

The uniform distribution refers to the equal value of random variables in a certain interval, for example, the bus departs from the terminal every hour every hour 10 minutes, and you randomly go to the station from 6:30 to 6:45 in the morning to take the bus, the arrival time is a random variable, and it obeys the uniform distribution, the density function is 1 15, and what is the probability that your waiting time is not more than 4 minutes?That is, to find the integral of the density function from 6:36 to 6:40, i.e., p=4 15

Therefore, the probability of a continuous random variable in an interval is the integral of the density function in this interval.