depthfirstlearning/depthfirstlearning.com

Error in Problem Set 1 2e?

RylanSchaeffer opened this issue · 9 comments

RylanSchaeffer commented

I think there may be an error in Problem Set 1 2e:

image

Specifically, x = phi(h), whereas the integrand term has phi(x). If this is a mistake, the problem is carried forward to

image

cinjon commented

Thanks Rylan, which curriculum is this?

cinjon commented

Sorry for the delay, and thanks for the bump! I'm not so familiar with this one, will ping the authors right now.

RylanSchaeffer commented
ramasesh commented

Hi Ryan,
Thanks for the question! I think I see the confusion. Though I think the expression is still correct, we used bad notation in writing $x$ as the variable of integration. In the equation with integration over $x$, this $x$ is just a dummy variable, not the same $x$ as $x^{l-1}_i$.

Does this clear things up? If so, we should probably change that expression to give the dummy variable a different name, maybe $h$.

Cheers,
Vinay

RylanSchaeffer commented

Ok thank you for clarifying! I'm still a bit confused by the notation $p_{h^{l-1}}(x)$ inside the integral. What does this notation for a density mean?

ramasesh commented

Oh, I see. Yeah, good question, let me try and explain. In this notation, $p_{h^{l-1}}(x)$ means "the probability density function of the random variable $h^{l-1}$, evaluated at value $x$". So $h^{l-1}$ is the random variable, and the probability of it taking on a value between, say, $4$ and $4 + \epsilon$ is $p_{h^{l-1}}(4)\times\epsilon$. Does this help?

RylanSchaeffer commented

Yep! Thank you for clarifying!