In the simplest setting, a continuous random variable is one that can assume any value on some interval of the real numbers.
For example, a uniform random variable is often defined on the unit interval [0,1], which means that this random variable could assume any value between 0 and 1, including 0 and 1. Some possibilities would be 1/3, 0.3214, pi/4, e/5, and so on ... in other words, any of the numbers in that interval.
As another example, a normal random variable can assume any value between -infinity and +infinity (another interval). Most of these values would be extremely unlikely to occur but they would be possible. The random variable could assume values of 3, -10000, pi, 1000*pi, e*e, ... any possible value in the real numbers.
It is also possible to define continue random variables that assume values on the entire (x,y) plane, or just on the circumference of a circle, or anywhere that you can imagine that is essentially equivalent (in some sense) to pieces of a real line.
It is a discrete random variable.
continuous random variable
Zero.
You integrate the probability distribution function to get the cumulative distribution function (cdf). Then find the value of the random variable for which cdf = 0.5.
A discrete random variable is a variable that can only take some selected values. The values that it can take may be infinite in number (eg the counting numbers), but unlike a continuous random variable, it cannot take any value in between valid results.
It is a discrete random variable.
True
Yes. It is a continuous variable. As used in probability theory, it is an example of a continuous random variable.
continuous random variable
Usually we consider a random variable which assigns a value to the outcome of an event. The value assigned to the outcome can be either discrete or continuous. The continuous random variable is a random variable whose domain is defined over a continuous range. Examples: Daily inches of rain, speed of cars on highway, purchases made everyday at grocery stores.
No. The probability that a continuous random variable takes a specific value is always zero.
it is a continuous random variable
Yes.
Zero.
it is a set of real numbers its consider fraction
You integrate the probability distribution function to get the cumulative distribution function (cdf). Then find the value of the random variable for which cdf = 0.5.
There is an exact number of miles for a given route on a trip. However, the measurement of the distance from the odometer some small and possibly random errors, so the measured distances could be considered a continuous random variable.