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Is it possible to generically describe the CDF of a finite length random sequence generated by storing the trajectory of a random walk?

For example, assume $X$ is an iid random variable with the cumulative distribution function $F_x(x)$ , $Y$ is a random sequence of length $N$ described by $y_{i+1} = y_i + x_i + c$ , where $c$ is a constant.

I want to develop an equation of the form $F_y(y) = func(F_x,N,c)$ .

Is this even possible?

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