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# Continuous Random Variable

In mathematics, random variable is a variable whose value is not fixed. It is subjected to change due to the change in circumstances or due to the randomness.
There are two types of random variables in statistics: Continuous and discrete.Here, we are going to discuss about continuous random variables.

Continuous Random Variables: These variables are the members of an uncountable continuous set of numbers. Continuous random variables can assign any random value within them.

For example:

• Height and weight records are continuous variables because these can take any value.
• Temperature record for few successive days for a particular city are continuous random variables.
Continuous random variable may take any value between its predefined upper and lower limits. It is not defined at a particular point. Instead, it is defined over an interval. Continuous random variable can be qualitative or quantitative.

Probability distribution evaluates the probability a particular event predefined over the space of an interval.

Let us consider X as a set of all possible values of continuous random variable. Probability density function of continuous random variable "X" is represented by f(x). Here, X is defined over the interval (a, b) and $x\in X$. Then:
• $f(x)\geq 0$, for all $x\in X$.
• $\int_{a}^{b}f(x)dx=1$.
• Probability that random variable takes a value between a and b is: $P(c< X< d)=\int_{c}^{d}f(x)dx,\ for\ a\leq c< d\leq b$.

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