#### kokokosini123

##### Newbie level 6

**Fig(1).**

The width of the time interval Δtk can be calculated by \( Δt_k=(N_k-1)T_0+Δt'+(T_0-Δt'')=N_kT_0+Δ_q\\where Δ_q=Δt'-Δt'' \)

The errors Δt' and Δt'' can be considered as random variables independent of each other that range from 0 to T0 and from -T0 to 0 with PDFs shown in Fig(2). And the sum of them is the convolution of their PDF as shown in fig(3).

**Fig(2).**

**Fig(3).**

Now I need to calculate the duty ratio of the square wave which is \[ \frac{Δt_k}{Δt_k+Δt_{k+1}} \] what is the PDF of the final result?