Let \(F(x)\) and \(f(x)\) be the respective distribution function and the probability density of a random variable \(X\). Answer with yes or no the following questions:

(1) \(F(x)\) and \(f(x)\) can be arbitrary real functions.

(2) \(f(x)\) is a nondecreasing function.

(3) \(f(x)\) cannot have jumps.

(4) \(f(x)\) cannot be negative.

(5) \(F(x)\) is always a continuous function.

(6) \(F(x)\) can assume values between -1 and +1 .

(7) The area between the abscissa and the graph of \(F(x)\) is always equal to 1 .

(8) \(f(x)\) must always be smaller than 1 .

(9) The area between the abscissa and the graph of \(f(x)\) is always equal to 1 .

(10) The properties of \(F(x)\) and \(f(x)\) are all the same to me.