Show that conditional variance of error in linear probability model is heteroskedastic? I have a problem that asks me the following:

&quot; Consider the linear probability model, in which we specify the
regression equation to be linear in X,
E(Y |X = x) = Pr(Y = 1|X = x) = x'β
We can accordingly express the regression equation by Y = X'β + e with
E(e |X = x) = 0 for all x. Show that the conditional variance of e
given X = x depends on x, i.e., e is heteroskedastic. &quot;

Intuitively, I visualise why this is the case - but cannot figure out how to demonstrate this formally. Could someone help?
Thanks in advance!
In relation to the problem of heteroskedasticity in linear probability models, the following Ben Lambert video is a useful link:
youtube.com/watch?v=pgPhbVEbYqw