p sample, july 18

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

See here.

date page question duration ans result thoughts
2025-07-18 Fri 13:13 44 98 4 b
99 7 e
167 406 10 e
407 8 c E median, not mean; also forgot variance
216 525 9 b
526 6 e C
102 241 12 e
242 5 b E

What the heck, man?

407. A memoryless distribution.

I had the right logic here. But I missed that the parameter in the question was the median rather than the mean. Argh.

526. Many zones with tornado risk.

Wrong result for the variance of many groups. I knew this one. I got it right before. But this time I messed it up.

Remind myself again. Expectation values go like

$$\begin{aligned} E(aX + b) = a\, E(X) + b \\ \end{aligned}$$

Oh, I see what I misremembered. For the independent systems, the variances add linearly.

Blugh.

242. A combined continuous $\times$ discrete distribution

I use the variance when I should have used the "second moment."