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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.
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For a continuous random variable the probability that the value of x is greater than a given constant is?
The integral of the density function from the given point upwards.
What is the formula for a random variable?
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.
Can the Poisson distribution be a continuous random variable or a discrete random variable?
True
Is temperature an example of continuous variable?
Yes. It is a continuous variable. As used in probability theory, it is an example of a continuous random variable.
What is the difference between a discrete and a continuous probability function?
A discrete random variable (RV) can only take a selected number of values whereas a continuous rv can take infinitely many.
