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One paragraph notes on Continuous Random Variables - Cumulative Distribution Function has to be own words...

One paragraph notes on Continuous Random Variables - Cumulative Distribution Function has to be own words not copy paste..

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A random variable X is said to be continuous if its space is either an interval or a union of intervals.A continuous random variable is a random variable where the data can take infinitely many values.

In other word we can also say that, A random variable X is said to be a continuous random variable if there exists a continuous function f:R- [0,infinity] such that for every set of real numbers A

P(XEA)=

For any continuous random variable with probability density function f(x), we have that:

And,

The cumulative distribution function (CDF) of a random variable is another method to describe the distribution of random variables. The advantage of the CDF is that it can be defined for any kind of random variable (discrete, continuous, and mixed).

The cumulative distribution function (CDF) of random variable X is defined as

FX(x)=P(X≤x), for all x∈R.

For all a≤ba≤b, we have

P(a<X≤b)=FX(b)−FX(a)

orchestra answered 1 year ago
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