Activity for DNB
| Type | On... | Excerpt | Status | Date |
|---|---|---|---|---|
| Edit | Post #283260 |
Post edited: |
— | over 3 years ago |
| Edit | Post #283291 | Initial revision | — | over 3 years ago |
| Question | — |
Why was my question closed: If Alice must've have classes on at least 2 days, why do you need the intersection of 3 's? 1. I don't know why the MathJax isn't processing at https://math.codidact.com/posts/282645. 2. But why was it closed "as not constructive"? >This question cannot be answered in a way that is helpful to anyone. It's not possible to learn something from possible answers, except for the solution... (more) |
— | over 3 years ago |
| Edit | Post #283115 |
Post edited: |
— | over 3 years ago |
| Comment | Post #282945 |
1. Thanks for your answer. I agree that P(A) + P(B) can $>1$, but then why can't we change the definition of probability to include all numbers $>1$? 2. "here is a simple geometric interpretation". This is just the area, correct? But how does this answer my question? (more) |
— | over 3 years ago |
| Comment | Post #283260 |
Thanks! Boy am I scatter brained! I already got one downvote here. If I keep getting downvotes, I'll construe them to mean that this question is too half-baked, and I'll delete (more) |
— | over 3 years ago |
| Comment | Post #282665 |
2. Why does "starting with the red equation would only prove that the green equation holds for odd n"? I see no thing in your last summation, or $0 \le k \le 2n + 1$ (the summation bounds) that restricts $k$ to odd integers? (more) |
— | over 3 years ago |
| Comment | Post #282665 |
Thanks. 1. How do I prove that $\{2n + 1 - k \mid k \in \{ 0,\dots,n \}\} \equiv \{n + 1,\dots, 2n + 1\}$? Undeniably, I can see that this is true if I substitute $k = 0,\dots,n$, because $2n + 1 - \color{red}0, 2n + 1 - \color{red}1, \dots, 2n + 1 - \color{red}n = 2n + 1, 2n, \dots, n + 1$. But thi... (more) |
— | over 3 years ago |
| Edit | Post #283260 |
Post edited: |
— | over 3 years ago |
| Edit | Post #283260 | Initial revision | — | over 3 years ago |
| Question | — |
How would you vaticinate to $-w_k$ from both sides of $w_{k + 1} = \dfrac{w_k - (1 - p)w_{k - 1}}{p}$? This question appeared on my pop quiz last week. I got 0%. I achieved everything until the green equation, then I didn't know how to proceed. After reading this solution, I see that you must isolate $pw{k + 1}$ and move $wk$ to the right. $\color{limegreen}{wk = pw{k + 1} + (1- p)w{k - 1}} \if... (more) |
— | over 3 years ago |
| Edit | Post #283255 |
Post edited: |
— | over 3 years ago |
| Edit | Post #283255 | Initial revision | — | over 3 years ago |
| Question | — |
After $n - 2$ unchosen doors are opened, how does the probability of the $n - 2$ unchosen doors "shift" or "transfer" to the lone unchosen door? The second quotation below uses the verb "shift" to describe how Monty Hall's opening the 98 unchosen doors (revealing a goat each) ""shifts" [boldening mine] that 99/100 chance to door #100"? The first quotation below uses "transfer". But how can probabilities "shift" or "transfer"? This analog... (more) |
— | over 3 years ago |
| Edit | Post #283254 |
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— | over 3 years ago |
| Edit | Post #283253 |
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— | over 3 years ago |
| Edit | Post #283254 |
Post edited: |
— | over 3 years ago |
| Edit | Post #283254 | Initial revision | — | over 3 years ago |
| Question | — |
How to visualize multiplication in the Odds form of Bayes's Theorem? Here I'm asking solely about the circle pictograms. Please eschew numbers as much as possible. Please explain using solely the circle pictograms. Undeniably, I'm NOT asking about how to multiply numbers. I don't understand Image alt text 1. How do I "visually" multiply Circle 1 (representing ... (more) |
— | over 3 years ago |
| Edit | Post #283253 |
Post edited: |
— | over 3 years ago |
| Edit | Post #283253 |
Post edited: |
— | over 3 years ago |
| Edit | Post #283253 |
Post edited: |
— | over 3 years ago |
| Edit | Post #283253 | Initial revision | — | over 3 years ago |
| Question | — |
How to visualize division in the Odds form of Bayes's Theorem? Here I'm asking solely about the circle pictograms. Please eschew referring to, or using, numbers as much as possible. Please explain using solely the circle pictograms. Undeniably, I'm NOT asking about how to divide numbers. I don't understand Image alt text 1. How do I "visually" divide Cir... (more) |
— | over 3 years ago |
| Edit | Post #283111 |
Post edited: |
— | over 3 years ago |
| Edit | Post #283252 | Initial revision | — | over 3 years ago |
| Question | — |
Which vertical line signifies "putting the cutoff for a positive result at a very low level"? The author, Karen Stewart MA Natural Sciences (Univ. of Cambridge) PhD Veterinary Microbiology (Cambridge), refers to "a purple dashed line" in her original graph, but I don't see any PURPLE dashed line. Perhaps I need an eye exam! So I re-colored and annotated them. Which of the 3 lines did she mean... (more) |
— | over 3 years ago |
| Comment | Post #282975 |
Thanks. Can you please recapitulate and underscore my mistake? I read your answer, but I still don't see my mistake? Perhaps you are too diplomatic to chide me, but go ahead! (more) |
— | over 3 years ago |
| Edit | Post #283118 |
Post edited: |
— | over 3 years ago |
| Edit | Post #283118 | Initial revision | — | over 3 years ago |
| Question | — |
Why would skyrocketing the numbers of doors help laypeople intuit the Monty Hall Problem? Alas, it isn't clear to me that it becomes clear that the probabilities are not 50-50 for the two unopened doors. Had I never seen this exercise or problem, even if there were 1 Billion doors, I would "stubbornly stick with their original choice". What am I misunderstanding? Am I just that witles... (more) |
— | over 3 years ago |
| Edit | Post #283116 | Initial revision | — | over 3 years ago |
| Question | — |
Intuitively, why would organisms — that after one minute, will either die, split into two, or stay the same, with equal probability — all die ultimately? I have no questions on the solution or the algebra, but even after re-reading the solution, I still can't fathom or intuit why $P(D) = 1$ from the problem statement. Even now, I couldn't have divined or foretold that $P(D) = 1$! Image alt text >The strategy of first-step analysis works here be... (more) |
— | over 3 years ago |
| Edit | Post #283115 | Initial revision | — | over 3 years ago |
| Question | — |
How does P(Monty opens door 2) = P(Monty opens door 3), and $P(\text{get car}|M_2)P(M_2) = P(\text{get car}|M_3)P(M_3)$? "Monty, who knows where the car is, then opens one of the two remaining doors. The door he opens always has a goat behind it (he never reveals the car!)." So Monty must open ONE of the $Mj (j = 2,3$), the one with the goat! But Monty mustn't and won't open the other $Mj$ with the car. So $P(M2) \neq ... (more) |
— | over 3 years ago |
| Edit | Post #283113 | Initial revision | — | over 3 years ago |
| Question | — |
In the Monty Hall problem, why can you just assume the contestant picked door 1? Why are you entitled to relabel the doors, or rewrite this solution with the door numbers permuted? My bafflement ought be obvious. 1. A contestant could've picked doors 2, 3. So you can't just assume he picked door 1. 2. Correct me if I'm wrong, but the game show didn't authorize contestants "to relabel the doors, or" permute the door numbers. So what permits you to do any of this in this solut... (more) |
— | over 3 years ago |
| Comment | Post #282600 |
That question got removed, and your link no longer works. (more) |
— | over 3 years ago |
| Edit | Post #283112 |
Post edited: |
— | over 3 years ago |
| Edit | Post #283112 |
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— | over 3 years ago |
| Edit | Post #283112 |
Post edited: |
— | over 3 years ago |
| Edit | Post #283112 | Initial revision | — | over 3 years ago |
| Question | — |
If a 2nd test's independent from the 1st test, then why does $\frac{0.95}{0.05}$ figure twice in $\frac{P(D|T_1)}{P(D^C|T_1)}\frac{P(T_2|D,T_1)}{P(T_2|D^C,T_1)}$? The problem statement postulates that "The new test is independent of the original test (given his disease status)". So where did the two $\frac{0.95}{ 0.05}$, that I underlined in red and purple, stem from? >### Example 2.6.1 (Testing for a rare disease, continued). >Fred, who tested posi... (more) |
— | over 3 years ago |
| Edit | Post #283111 | Initial revision | — | over 3 years ago |
| Question | — |
Why's the true positive rate termed Sensitivity and true negative rate Specificity, not vice versa? 1. To wit, what's "Sensitive" about True Positive Rates, and "Specific" about True Negative Rates? 2. Why weren't these Metaphors) or Imports reversed? Why wasn't "Sensitive" termed to signify True Negative Rates, and "Specific" True Positive Rates instead? I learn best visually. Can these g... (more) |
— | over 3 years ago |
| Edit | Post #283110 |
Post edited: |
— | over 3 years ago |
| Edit | Post #283110 | Initial revision | — | over 3 years ago |
| Question | — |
How do these 3 bell curves of Likelihood, Posterior, Prior pictorialize the Odds form of Bayes' rule? I learn best visually, and I found these graph. 1. Does it furnish intuition on Theorem 2.3.5 below? 2. E.g. Is the Likelihood Ratio always graphically left of Posterior and Prior? If so, why? >This can also be pictorially represented – the graph below shows the new posterior belief for a cer... (more) |
— | over 3 years ago |
| Edit | Post #282966 | Initial revision | — | over 3 years ago |
| Question | — |
What's wrong with evaluating $n(n-1) \dots (n-[k-3])(n-[k-2])\color{red}{(n-[k-1])}$ at $k = 1$? This snag arose out of this post, and these comments by r. In that post, I couldn't imagine how >By convention, $n(n-1) \dots {\color{red}{(n-k+1)}} = n$ for k = 1. Thus I wrote out the LHS $= n(n-1)(n - 2) \dots (n-[k-3])(n-[k-2])\color{red}{(n-[k-1])}$. Then I substituted $k=1$ into this exp... (more) |
— | over 3 years ago |