Probability distribution of continuous random variable is called as probability density function or pdf. In probability theory a probability density function or density of a continuous random variable is a function whose value at any given sample in the sample space can be interpreted as providing a relative likelihood that the value of the random variable would equal that sample.
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Examples include the height of an adult picked at random from a population or the amount of time that a taxi driver has to wait before their next job.
Probability distribution function vs density. In other words while the absolute likelihood for a continuous random variable to take on any particular value is 0 the value of the pdf at two different samples can be used to infer in any particular draw of the ran. Given the probability function px for a random variable x the probability that x belongs to a where a is some interval is calculated by integrating px over the set a ie. Probability distribution function and probability density function are functions defined over the sample space to assign the relevant probability value to each element.
Sometimes we are concerned with the probabilities of random variables that have continuous outcomes. Cumulative distribution functions cdfs recall definition 322 the definition of the cdf which applies to both discrete and continuous random variablesfor continuous random variables we can further specify how to calculate the cdf with a formula as follows. It is important to say that probability distribution function is a probability ie its value is a number between 0 and one and it is defined for both discrete and continuous random variables.
This statistics video tutorial provides a basic introduction into cumulative distribution functions and probability density functions. So one might interpret that probability distribution describes perhaps a member of a family of distributions density can be used for discrete distributions like the binomial and the phrase distribution function might be preferred over distribution when the cumulative distribution function is what is intended. Probability distribution functions are defined for the discrete random variables while probability density functions are defined for the continuous random variables.
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