A discrete random variable is a random variable that has countable values such as a list of non negative integers. The difference between discrete an continuous variables are just a matter of convenience and you can treat a variable as discrete even if it takes negative values.
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These distributions may apply to unobservable events or conditional probabilities.
Can continuous probability distribution be negative. Thus a discrete probability distribution is often presented in tabular form. Further we know that the area under the curve from negative infinity to positive infinity is one. The probability of the outcome of an experiment is never negative although a quasiprobability distribution allows a negative probability or quasiprobability for some events.
In summary and returning to the question. This probability is always positive. The beta negative binomial distribution.
A discrete distribution can only take a limited set of values whereas continuous distributions can take in any value within the specified range. This means the set of possible values is written as an interval such as negative infinity to positive infinity zero to infinity or an interval like 0 10 which. The boltzmann distribution a discrete distribution important in statistical physics which describes the probabilities of the various discrete energy levels of a system in thermal equilibriumit has a continuous analogue.
With a discrete probability distribution each possible value of the discrete random variable can be associated with a non zero probability. You just need it to take few enough values to be interested in frequency of each one. The continuous distributions are represented in terms of probability density as there can be infinite values in a certain range and the probability of each value will be zero.
A continuous distributions probability function takes the form of a continuous curve and its random variable takes on an uncountably infinite number of possible values. The main difference between continuous and discrete distributions is that continuous distributions deal with a sample size so large that its random variable values are treated on a continuum from negative infinity to positive infinity while discrete distributions deal with smaller sample populations and thus cannot be treated as if they are on a continuum. The normal probability distribution one of the fundamental continuous distributions of statistics is actually a family of distributions an infinite number of distributions with differing means m and standard deviations s.
The probability density function of a continuous random variable expresses the rate of change in the probability distribution over the range of potential continuous values defined and expresses.
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