Probability density function
The probability density function f(x) describes the distribution of probability for a continuous random variable. It has the properties
With a continuous random variable, the probability that X=x is always 0. It is only meaningful to speak about the probability that X lies in an interval P[X=x]=0, if X is a continuous random variable.
When determining the probability of an interval a to b, we need not be
concerned if either or both end points are included in the interval. Since the
probabilities of X=a and X=b are both equal to 0,
The standarized variable
has mean 0 and sd 1.