In this question we will compute red, green and blue pixel values in the manner described in class. Specifically, given a spectral irradiance function I$($x$),$ a spectral albedo function A$($x$),$ and specifications of the sensor response functions for each of three color bands, e$.$g$.$ Sr$($x$),$ Sg$($x$),$ Sb$($x$),$ where variable x stands for wavelength, then the measured R$,$G$,$B intensity values can be computed as R $=$ Z $700$ x$=400$ I$($x$)$A$($x$)$Sr$($x$)$dx $(1)$ G $=$ Z $700$ x$=400$ I$($x$)$A$($x$)$Sg$($x$)$dx $(2)$ B $=$ Z $700$ x$=400$ I$($x$)$A$($x$)$Sb$($x$)$dx $(3)$ a$12$ a$13$ a$22$ a$2301$ f $0000$ f $000010$ r$11$ r$12$ r$130$ r$21$ r$22$ r$230$ r$31$ r$32$ r$3300001100$ cx $010$ cy $001$ cz $0001$ P$($xt$|$ Zt$1)=$ Z P$($xt$|$xt$1)$P$($xt$1|$ Zt$1)$dxt$1$ P$($xt$|$ Zt $)=$ P$($zt$|$xt$)$P$($xt$|$ Zt$1)$ P$($zt$|$ Zt$1)$ P$($zt$|$ Zt$1)=$ Z P$($zt$|$xt$)$P$($xt$|$ Zt$1))$dxt $|$Zt $)=$ cP$($zt$|$xt$)$ Z P$($xt$|$xt$1)$P$($xt$1|$ Zt$1)$dxt$11$ Compute R$,$G$,$B values for the following combination of irradiance, albedo, and sensor response functions. B $=$ Z $700$ x$=400$ I$($x$)$A$($x$)$Sb$($x$)$dx $(1)$ G $=$ Z $700$ x$=400$ I$($x$)$A$($x$)$Sg$($x$)$dx $(2)$ R $=$ Z $700$ x$=400$ I$($x$)$A$($x$)$Sr$($x$)$dx $(3)$ I$($x$)=0\mathrm{.}5400<$ x $<=6001\mathrm{.}0600<$ x $<=7000$ otherwise A$($x$)=1100($x$400)400<$ x $<=5001\mathrm{.}0500<$ x $<=7000$ otherwise Sb$($x$)=1\mathrm{.}0400<$ x $<=5000$ otherwise Sg$($x$)=1\mathrm{.}0500<$ x $<=6000$ otherwise Sr$($x$)=1\mathrm{.}0600<$ x $<=7000$ otherwise $1$ B $=$ Z $700$ x$=400$ I$($x$)$A$($x$)$Sb$($x$)$dx $(1)$ G $=$ Z $700$ x$=400$ I$($x$)$A$($x$)$Sg$($x$)$dx $(2)$ R $=$ Z $700$ x$=400$ I$($x$)$A$($x$)$Sr$($x$)$dx $(3)$ I$($x$)=0\mathrm{.}5400<$ x $<=6001\mathrm{.}0600<$ x $<=7000$ otherwise A$($x$)=1100($x$400)400<$ x $<=5001\mathrm{.}0500<$ x $<=7000$ otherwise Sb$($x$)=1\mathrm{.}0400<$ x $<=5000$ otherwise Sg$($x$)=1\mathrm{.}0500<$ x $<=6000$ otherwise Sr$($x$)=1\mathrm{.}0600<$ x $<=7000$ otherwise $1$ Note that these are definite integrals, so they evaluate to specific numbers. R $=\_\_\_\_\_$ G $=\_\_\_\_\_$ B $=\_\_\_\_\_$