A 12-sided solid has faces numbered 1 to 12. The table shows the results of rolling the solid 200 times. Find the experimental
probability of rolling a number less than 3.
2 answers:
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1. By the chain rule,
I'm going to switch up the notation to save space, so for example, is shorthand for
.
We have
Similarly,
where
To capture all the partial derivatives of , compute its gradient:
2. The problem is asking for and
. But
is already a function of
, so the chain rule isn't needed here. I suspect it's supposed to say "find
and
" instead.
If that's the case, then
as the hint suggests. We have
Putting everything together, we get