Assuming a fully connected feedforward network where all the neurons uses a linear

activation function $($i$.$e$.,$ ai $$ zi$)$ and with the following topology:

$($a$)100$ neurons in the input layer

$($b$)5$ hidden layers with $2,000$ neurons in each layer

$($c$)10$ neurons in the output layer

If all the inputs to the network have been standardized to have a mean value of $0$ and

a standard deviation of $1,$ and the initial weights for the network are sampled from a

normal distribution with mean $0\mathrm{.}0$ and standard deviation of & $0\mathrm{.}01,$ then:

$($a$)$ Calculate the variance of the z values across for the neurons in the first hidden

layer in the first iteration of training.