Seemingly cultural fortune telling

The problem solving process is as follows:

Extended data

If the probability density function fX(x) is continuous at point X, then the cumulative distribution function is derivable.

Because the value of the random variable X depends only on the integral of the probability density function, the value of the probability density function of a single point will not affect the performance of the random variable. More precisely, if a function and the probability density function of X have only finite or countable points with different values, or the measure is 0 (a zero measure set) relative to the whole real number axis, then this function can also be the probability density function of X.

The probability that a continuous random variable takes a value at any point is zero. As a corollary, the probability that a continuous random variable takes a value on an interval has nothing to do with whether the interval is open or closed. It should be noted that the probability P{x=a}=0, but {x=a} is not an impossible event.