3. Let X=(Xt)t0 and Y=(Yt)t0 be square-integrable martingales with respect to the filtrations FtX=(Xuut) and FtY=(Yuut) generated by the processes, respectively, and let Ft=(Xu,Yuut) for t0. We want to show that if X and Y are independent, then the product XY is a martingale with respect to (Ft), through the following steps. a) Fix ts0, and let S={AFsE[XtYtIA]=E[XsYsIA]}. Show that S satisfies SA,BS,ABB\ASAnSincreasingnAnS a) Fix ts0, and let S={AFsE[XtYtIA]=E[XsYsIA]}. Show that S satisfies S A,BS,ABB\AS AnS increasing nAnS or Excel Oritire 3. Let X=(Xt)t0 and Y=(Yt)t0 be square-integrable martingales with respect to the filtrations FtX=(Xuut) and FtY=(Yuut) generated by the processes, respectively, and let Ft=(Xu,Yuut) for t0. We want to show that if X and Y are independent, then the product XY is a martingale with respect to (Ft), through the following steps. a) Fix ts0, and let S={AFsE[XtYtIA]=E[XsYsIA]}. Show that S satisfies SA,BS,ABB\ASAnSincreasingnAnS 3. Let X=(Xt)t0 and Y=(Yt)t0 be square-integrable martingales with respect to the filtrations FtX=(Xuut) and FtY=(Yuut) generated by the processes, respectively, and let Ft=(Xu,Yuut) for t0. We want to show that if X and Y are independent, then the product XY is a martingale with respect to (Ft), through the following steps. a) Fix ts0, and let S={AFsE[XtYtIA]=E[XsYsIA]}. Show that S satisfies SA,BS,ABB\ASAnSincreasingnAnS a) Fix ts0, and let S={AFsE[XtYtIA]=E[XsYsIA]}. Show that S satisfies S A,BS,ABB\AS AnS increasing nAnS or Excel Oritire 3. Let X=(Xt)t0 and Y=(Yt)t0 be square-integrable martingales with respect to the filtrations FtX=(Xuut) and FtY=(Yuut) generated by the processes, respectively, and let Ft=(Xu,Yuut) for t0. We want to show that if X and Y are independent, then the product XY is a martingale with respect to (Ft), through the following steps. a) Fix ts0, and let S={AFsE[XtYtIA]=E[XsYsIA]}. Show that S satisfies SA,BS,ABB\ASAnSincreasingnAnS