GATE Electronics and Communications (EC) 2022 Solved Paper

Consider a channel over which either symbol x_A or symbol x_B is transmitted. Let the output of channel Y be the input to a maximum likelihood (ML) detector at the receiver. The conditional probability density functions for 𝑌 given x_A and x_B are:
${\mathit{f}}_{\mathit{Y}|.{\mathit{x}}_{\mathit{A}}}\left(\mathit{y}\right)={\mathit{e}}^{-\left(\mathit{y}+1\right)}\mathit{u}\left(\mathit{y}+1\right)$
${\mathit{f}}_{\mathit{Y}|.{\mathit{x}}_{\mathit{B}}}\left(\mathit{y}\right)={\mathit{e}}^{\left(\mathit{y}-1\right)}\left(1-\mathit{u}\left(\mathit{y}-1\right)\right)$
where u(⋅) is the standard unit step function. The probability of symbol error for this system is _________ (rounded off to two decimal places).