Check whether by suitable choice of the parameter \(a\) the following functions are densities of random variables. If the answer is yes, determine the respective distribution functions, mean values, variances, medians, and modes.

(1) \(f(x)=a|x|,-3 \leq x \leq+3\),

(2) \(f(x)=a x e^{-x^{2}}, x \geq 0\),

(3) \(f(x)=a \sin x, 0 \leq x \leq \pi\),

(4) \(f(x)=a \cos x, 0 \leq x \leq \pi\).