Assume that y follows the Poisson distribution with mean λ. If the conditional distribution of X given Y = y is Uniform (0, y) for all y > 0, identify the moment generating function of X \((M(t) = E[e^tX]).\) Select the correct choice from the following option?
1
\( M(t) = \frac{λ}{(1 - e^t)}\)
2
\(M(t) =\frac{ λ}{(1 - λe^t)}\)
3
\( M(t) = e^λ(e^t - 1)\)
4
\(λe^{-(λ/2)e^t}\)