Q$1.$ We derived NP criteria using Gaussians. Now consider the case where a

matching is needed, for instance matching faces to determine a criminal, match$-$

ing unique ID number such as Aadhar, finding a transmitted radio signal in a

noisy environment. In all these cases, there are two possibilities, a match or no

match, that is two categories. Suppose when there is no match this class is ${}_1,$

and when match happens it is class ${}_1.$ One can have several samples and ob$-$

tain the distribution of these two classes. Let $p(x|{}_1)$ is standard Gaussian and

$p(x|{}_2)$ is exponential pdf $e^{-x}$ for $x0,$ and $0$ otherwise, $=0\mathrm{.}5.$ Suppose

the error rate for the case when observed sample $x$ belong to ${}_1$ but is classified

as ${}_2$ is $E_1=0\mathrm{.}1.$ Find the error rate when observed sample $x$ belongs to ${}_2$

but is classified as ${}_1.$