Table of Contents
Define Random Variable
A random variable is a function that assigns a real number to each outcome of an experiment. A random variable can be discrete or continuous. A discrete random variable assigns a unique number to each outcome. A continuous random variable assigns a real number to each outcome in an interval. Random Variables – Definition Uses Significance Types Solved Examples and FAQs.
Uses and Significance of Random Variable
A random variable is a function that assigns a real number to each outcome of an event. It is a tool used in probability theory to model the variability of a random phenomenon. A random variable can take on any of a continuum of possible values. The probability of any particular value is zero.
There are two types of random variables: discrete and continuous. A discrete random variable can take on only a finite number of values, while a continuous random variable can take on an infinite number of values.
Uses of random variables include:
Modeling the variability of a random phenomenon
Determining the probability of different outcomes
Calculating expected values and variances
Making decisions under uncertainty
The most important application of random variables is in the field of statistics. In particular, it is used to calculate the sampling distribution of a statistic, which is essential for doing hypothesis testing.
Types of Random Variables
There are two types of random variates: discrete and continuous.
A discrete random variate is a variable that can take on a finite or countable number of values. For example, the number of heads that result from flipping a coin n times is a discrete random variate. The probability of any given value is given by the relative frequency of that value in the long run.
A continuous random variate is a variable that can take on any value within a given interval. For example, the time it takes for a radioactive atom to decay is a continuous random variate. The probability of any given value is zero.
Random Variable In Probability
And Statistics
A random variable is a quantity that is determined by a random process. In probability and statistics, a random variable is a variable that represents the outcome of a random phenomenon.
Probability Distribution In Random Variable
A probability distribution in a random variable is a table that shows the probability of each possible value of the random variable.
Important Probability Distributions
The binomial distribution is used to model the number of successes in a sequence of Bernoulli trials.
The Poisson distribution is used to model the number of events occurring in a given time period.
The normal distribution is used to model continuous data.
Discrete Random Variable and Probability Distribution
A discrete random variable is a variable that can take on a certain, finite number of values. The probability distribution for a discrete random variable is a table that shows the probability of each possible value.
