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A discrete random variable (RV) can only take a selected number of values whereas a continuous rv can take infinitely many.

Q: What is the difference between a discrete and a continuous probability function?

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The formula, if any, depends on the probability distribution function for the variable. In the case of a discrete variable, X, this defines the probability that X = x. For a continuous variable, the probability density function is a continuous function, f(x), such that Pr(a < X < b) is the area under the function f, between a and b (or the definite integral or f, with respect to x, between a and b.

The graph of a continuous function will not have any 'breaks' or 'gaps' in it. You can draw it without lifting your pencil or pen. The graph of a discrete function will just be a set of lines.

Yes- the highest probability value is the mode. Let me clarify this answer: For a probability mass function for a discrete variables, the mode is the value with the highest probability as shown on the y axis. For a probability density function for continuous variables, the mode is the value with the highest probability density as shown on the y-axis.

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I am not quite sure what you are asking. If this answer is not complete, please be more specific. There are many probability density functions (pdf) of continuous variables, including the Normal, exponential, gamma, beta, log normal and Pareto. There are many links on the internet. I felt that the related link gives a very "common sense" approach to understanding pdf's and their relationship to probability of events. As explained in the video, a probability can be read directly from a discrete distribution (called a probability mass function) but in the case of a continuous variable, it is the area under the curve that represents probability.

Related questions

Demand schedule: a list of demand/price equivalencies. It can best be seen as a table with discrete points. Demand function: a continuous function of price-demand interaction. Main difference: schedule is discrete; function is continuous.

The probability mass function is used to characterize the distribution of discrete random variables, while the probability density function is used to characterize the distribution of absolutely continuous random variables. You might want to read more about this at www.statlect.com/prbdst1.htm (see the link below or on the right)

Normal distribution is the continuous probability distribution defined by the probability density function. While the binomial distribution is discrete.

I will assume that you are asking about probability distribution functions. There are two types: discrete and continuous. Some might argue that a third type exists, which is a mix of discrete and continuous distributions. When representing discrete random variables, the probability distribution is probability mass function or "pmf." For continuous distributions, the theoretical distribution is the probability density function or "pdf." Some textbooks will call pmf's as discrete probability distributions. Common pmf's are binomial, multinomial, uniform discrete and Poisson. Common pdf's are the uniform, normal, log-normal, and exponential. Two common pdf's used in sample size, hypothesis testing and confidence intervals are the "t distribution" and the chi-square. Finally, the F distribution is used in more advanced hypothesis testing and regression.

The formula, if any, depends on the probability distribution function for the variable. In the case of a discrete variable, X, this defines the probability that X = x. For a continuous variable, the probability density function is a continuous function, f(x), such that Pr(a < X < b) is the area under the function f, between a and b (or the definite integral or f, with respect to x, between a and b.

The graph of a continuous function will not have any 'breaks' or 'gaps' in it. You can draw it without lifting your pencil or pen. The graph of a discrete function will just be a set of lines.

Yes- the highest probability value is the mode. Let me clarify this answer: For a probability mass function for a discrete variables, the mode is the value with the highest probability as shown on the y axis. For a probability density function for continuous variables, the mode is the value with the highest probability density as shown on the y-axis.

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A random variable is a variable that can take different values according to a process, at least part of which is random.For a discrete random variable (RV), a probability distribution is a function that assigns, to each value of the RV, the probability that the RV takes that value.The probability of a continuous RV taking any specificvalue is always 0 and the distribution is a density function such that the probability of the RV taking a value between x and y is the area under the distribution function between x and y.

It is a function that gives the probabilities associated with the discrete number of values that a random variable can take.

I am not quite sure what you are asking. If this answer is not complete, please be more specific. There are many probability density functions (pdf) of continuous variables, including the Normal, exponential, gamma, beta, log normal and Pareto. There are many links on the internet. I felt that the related link gives a very "common sense" approach to understanding pdf's and their relationship to probability of events. As explained in the video, a probability can be read directly from a discrete distribution (called a probability mass function) but in the case of a continuous variable, it is the area under the curve that represents probability.

A convolution is a function defined on two functions f(.) and g(.). If the domains of these functions are continuous so that the convolution can be defined using an integral then the convolution is said to be continuous. If, on the other hand, the domaisn of the functions are discrete then the convolution would be defined as a sum and would be said to be discrete. For more information please see the wikipedia article about convolutions.