"A first Course in probability"-chaper4-continuous type random variable-basic concept

When we use the basic probability theory to solve practical problems, we can easily find some random variables of the continuous distribution, such as the time of the train station, the life of the lamp, and some time-related random variables, we found it difficult to find out the probability of a point, because the random variable is continuous, The basic event space is an infinite space, and with the infinite, continuous these words related, it is natural to think, here we need to use the tools of integration.

Now, the question is, how do we use points for this tool? We assume that a curve f (x) and a continuous random variable's value interval [A, a] is surrounded by a curved trapezoid with an area of 1 (the control area is 1 to satisfy the basic properties of the distribution column), then for P (c≤x≤d), it is equal to the definite integral of f (x) in [C,d].

It is easy to see the distribution column for different problems, so that the F (x) and the distribution columns in a curved edge ladder are themselves one by one mappings, we call F (x) the probability density curve of the continuous random variable x.

Based on these things, we can give a good definition of a continuous random variable next:

The random variable x that satisfies the distribution column of such a probability distribution becomes a continuous random variable (where B is the collection representing the range of values).

"A first Course in probability"-chaper4-continuous type random variable-basic concept