Question

How do you find P(X=x)

Answer 1

A continuous random variable takes on an uncountably infinite number of possible values. For a discrete random variable X that takes on a finite or countably infinite number of possible values, we determined P(X = x) for all of the possible values of X, and called it the probability mass function ("p.m.f."). For continuous random variables, as we shall soon see, the probability that X takes on any particular value x is 0. That is, finding P(X = x) for a continuous random variable X is not going to work. Instead, we'll need to find the probability that X falls in some interval (a, b), that is, we'll need to find P(a < X < b). We'll do that using a probability density function ("p.d.f."). We'll first motivate a p.d.f. with an example, and then we'll formally define it.

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