Analytically derive the Probability Density function for the following, where A(?) ~ ?[1,5], ?(?) ~ U[0,1] and C(?) ~ Exponential(?=3)

. A simple linear scaling Y1(S; t) = A($)t . An affine transformation Y2 ( 5; t) = A(5)t + C(5) . A sinusoid with a random amplitude and a random phase Y3(S; t) = A(5) cos(wt + 2n B(S) ) . A sawtooth wave with a random amplitude H YA(Sit) = 2A(5) 2TT NO 2 TTo A step function with a random trigger time, random amplitude, and random oset Y6K; 15) : A(C)u(t 0(0) 3(6)