p sample, july 2

$ \gdef\and{\cap} \gdef\or{\cup} \gdef\bar#1{\overline{#1}} $

See here.

Nailed it today.

The big takeaway is that I have finally had a session where I got all of the conditional-probability questions correct. I had to make a big table in every case.

Question 499 would have been more straightforward if I had known the form of the cumulative probability for the Poisson distribution, instead of having to program my calculator to compute it by summing the probability density. Is that straightforward? When I practiced writing down the discrete distributions, I only included one CDF, and it wasn't that one.

Well, perhaps I did look at it and decide not to care. The Wikipedia page currently says $$\begin{aligned} F(k) &= \frac{\Gamma(k+1, \lambda)}{k!} = e^{-\lambda}\sum_{j=0}^k \frac{\lambda^j}{j!} \end{aligned}$$

which is, in the first case, some wacky special function, and in the second case just doing the sum yourself.

One hour on these problems today: forty minutes to do them, and twenty minutes to write them up.