Suppose you have a dataset x$1,...,$ xn$,$ and you double the size of the dataset by adding each data point

twice. Answer the below questions about what happens to the behavior of SGD$,$ minibatch SGD $($for a

fixed batch size m$),$ and gradient descent.

$1.$ What happens to the cost per iteration of each method?

$2.$ What happens to the expected value of the gradient estimate for SGD and minibatch SGD$?$

$3.$ What happens to the variance of the gradient estimator for SGD and minibatch SGD$?$