How Much Dropout Wobbles a Sum

A hidden layer produces three activations for one training example:

$\mathbf{h} = [\,2.0,\; 3.0,\; 6.0\,]$

A single downstream unit simply adds them up (all weights equal $1$, no bias), producing $S$.

During training, inverted dropout with keep probability $q = 0.80$ is applied to the layer. Each unit gets its own independent mask $r_i \sim \text{Bernoulli}(q)$, and surviving units are rescaled:

$\tilde{h}_i = \frac{h_i \, r_i}{q}, \qquad S = \sum_{i=1}^{3} \tilde{h}_i$

The activations $\mathbf{h}$ are fixed; the only randomness is the mask.

Over the randomness of the masks, what are the mean and the standard deviation of $S$?