What is the meaning of random variable?

What is the meaning of random variable?

A random variable is a variable whose value is unknown or a function that assigns values to each of an experiment’s outcomes. A random variable can be either discrete (having specific values) or continuous (any value in a continuous range).

What is meant by random experiment?

In particular, a random experiment is a process by which we observe something uncertain. After the experiment, the result of the random experiment is known. An outcome is a result of a random experiment. The set of all possible outcomes is called the sample space.

What is meant by a random variable Chapter 16?

random variable- a value based on the outcome of a random event. random variables are denoted by a capital letter such as X. continuous random variable- a random variable that can take any numeric value within a range of values. the range may be infinite or bounded at either or both ends.

What are the characteristics of a random variable?

In probability theory and statistics, the characteristic function of any real-valued random variable completely defines its probability distribution. If a random variable admits a probability density function, then the characteristic function is the Fourier transform of the probability density function.

What values may the random variable assume?

The expected value, or mean, of a random variable—denoted by E(x) or μ—is a weighted average of the values the random variable may assume. In the discrete case the weights are given by the probability mass function, and in the continuous case the weights are given by the probability density function.

What are the characteristics of this random variable?

The characteristic function of a real-valued random variable always exists,since it is an integral of a bounded continuous function over a space whose measure is finite.

A characteristic function is uniformly continuous on the entire space

It is non-vanishing in a region around zero: φ (0) = 1.

It is bounded:|φ ( t )|≤ 1.

How do you calculate the variance of a random variable?

For a discrete random variable the variance is calculated by summing the product of the square of the difference between the value of the random variable and the expected value, and the associated probability of the value of the random variable, taken over all of the values of the random variable. In symbols, Var(X) = (x – µ)2 P(X = x)