How To Build A Distribution Function | The Science

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# How to build a distribution function

The distribution of the random variable - a ratio which establishes a link between the possible values ​​of a random variable and the probability of their appearance in the trial. We know three basic laws of distribution of random variables: number of probability distribution (for discrete random variables), distribution function, probability density.

## Instruction how to build a distribution function

Step 1:

The distribution function (sometimes - integral distribution law) - a universal law of distribution suitable for probabilistic description of both discrete and continuous ST A (random variables). Determined as a function of the argument x (maybe its possible value of X = x), which is equal to F (x) = P (X

Step 2:

Consider the task of building F (x) of a discrete random variable X is given by a series of probabilities and presented polygon distribution in Figure 1. For the sake of simplicity with 4 possible values.

Step 3:

When H≤x1 F (x) = 0, since event {X

Step 4:

When Xgt; x4 F (x) = p1 + p2 + p3 + p4 = 1 (according to the normalizing condition). Another explanation is - in this case, the event {x

Step 5:

For discrete CB having values ​​of n, the number of "steps" in the graph of the distribution function, obviously, will be equal to n. When the n, tends to infinity, assuming that discrete point "completely" fill the whole real line (or portion thereof), we see that the graph of the distribution function appears more and more steps, all the smaller ( "creeping", by the way, up), which limit a moving continuous line, which forms a continuous schedule random variable function.

Step 6:

It is worth noting that the basic property of the distribution function: P (x1≤X