Suppose we want to implement a dropout layer for a dense hidden layer $l$ of a deep neural network with a dropout probability of $0\mathrm{.}2.$ Consider

the following dropout$-$matrix:

$D=\left[\begin{array}{cccc}0\mathrm{.}49& 0\mathrm{.}47& 0\mathrm{.}7& 0\mathrm{.}99\\ 0\mathrm{.}86& 0\mathrm{.}49& 0\mathrm{.}76& 0\mathrm{.}96\\ 0\mathrm{.}13& 0\mathrm{.}98& 0\mathrm{.}07& 0\mathrm{.}54\\ 0\mathrm{.}48& 0\mathrm{.}96& 0\mathrm{.}76& 0\mathrm{.}32\end{array}\right]$

$($a$)$ What is the number of nodes in dense layer $l?$

$($b$)$ What is the batch size?

$($c$)$ Each batch sample contributes to the learning of specific nodes of dense layer $l.$ Identify those for each batch sample.

$($d$)$ Write down the forward propagation equation through the dropout layer for each batch sample.