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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.
What is the mean of frequency distribution?
It is a mathematically calculated summary statistic. With discrete distributions it is the arithmetic mean whereas with a continuous distribution it is the value of the random variable (RV) such that it divides the area under the probability distribution curve in half.
Density function of a continuous random variable?
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.
What is the formula for figuring out probability?
For a discrete distribution, if n trials are carried out and if x of them are favourable to the event that you are interested in, then the probability is x/n. Note that it may be possible to work out n and x on theoretical grounds rather than actually doing the experiment. The formula gets more complicated for continuous variables. For continuous variables, it is the area under the probability density curve over the domain of interest.
What does the probability density function tell you?
The area under the pdf between two values is the probability that the random variable lies between those two values.
