F(x) = Pr[X<=x] for x in the domain of the random variable
If the random variable is a discrete random variable, all of the probability is concentrated on a discrete set of points. We can define the probability for a specific point by the [probability mass function]?.
p(x) = limit{F(x+t)-F(x-t)} as t goes to zero.
For a continuous random variable, we define the [probability density function]? (at x) by
dF(x) F(x+t) - F(x) f(x) = ----- = limit ------------- as t goes to zero. dx t
Several probability distributions are so important that they have been given specific names, the normal distribution, the binomial distribution, the [Poisson distribution]? are just three of them.
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