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by Paul
May 22nd, 2020, 2:43 am
Forum: Off Topic
Topic: Is everyone ok?
Replies: 42
Views: 3772

Re: Is everyone ok?

Perhaps it's time for an update in this particular thread. I've now recovered at home for a few weeks and have improved to the point of being able to walk around the (long NYC) block and, with some trepidation, up a flight of stairs. 
Excellent news! Now just don't get mugged!
by Paul
May 19th, 2020, 5:22 pm
Forum: Off Topic
Topic: Good things that come out of this pandemic...
Replies: 249
Views: 14940

Re: Good things that come out of this pandemic...

78. Moderna's news is good

mRNA [$]\rightarrow[$]  Moderna -- nice. 
Let's hope "what is mRNA-1273?" one day becomes a Jeopardy answer!
When capitalism is destroyed who is going to find the vaccine for the next (A.k.a. final) pandemic?
by Paul
May 18th, 2020, 9:51 pm
Forum: Numerical Methods Forum
Topic: Models for Covid-19
Replies: 420
Views: 24093

Re: Models for Covid-19

I like it! I think I’ll diversify, catch a little bit of this, a little bit of that.

We have risk-neutral rate of infection, certainty equivalent, implied rates, and I’m sure we can back out the hospital price of risk.
by Paul
May 18th, 2020, 4:14 pm
Forum: Off Topic
Topic: Bad things that come out of this pandemic
Replies: 83
Views: 8867

Re: Bad things that come out of this pandemic

That was my conclusion too.
by Paul
May 17th, 2020, 10:00 pm
Forum: Off Topic
Topic: Bad things that come out of this pandemic
Replies: 83
Views: 8867

Re: Bad things that come out of this pandemic

Another luvvie, Neil Gaiman, comes out as hypocrite; the lockdown rules don't apply to him natch. (I've only read one of his books. Guardian readers probably say "deep and meaningful." I say "trite and childish.")
by Paul
May 17th, 2020, 7:33 pm
Forum: Numerical Methods Forum
Topic: Models for Covid-19
Replies: 420
Views: 24093

Re: Models for Covid-19

Not unrelated: I've started to read (sorry haven't saved any refs) that R_0 isn't necessarily the greatest thing since sliced bread (no kidding!), and even that R_0 going above one might not matter, something about variability in R_0 makes things safer. I am confused. If you have a simple exponentia...
by Paul
May 17th, 2020, 4:12 pm
Forum: Off Topic
Topic: Good things that come out of this pandemic...
Replies: 249
Views: 14940

Re: Good things that come out of this pandemic...

77. They'll probably find a cure/vaccine for the common cold.
by Paul
May 16th, 2020, 10:39 pm
Forum: Brainteaser Forum
Topic: expected number of 1-runs
Replies: 32
Views: 7146

Re: expected number of 1-runs

Ends in:

HH then H No change
HH then T No change
HT then H +1
HT then T No change
TH then H -1
TH then T No change
TT then H +1
TT then T No change

Expectation goes up by 1/8

N runs then also easy.

Standard deviation similar. Exercise for the reader!
by Paul
May 16th, 2020, 9:24 pm
Forum: Numerical Methods Forum
Topic: Models for Covid-19
Replies: 420
Views: 24093

Re: Models for Covid-19

They're the same.
by Paul
May 16th, 2020, 5:10 pm
Forum: Brainteaser Forum
Topic: expected number of 1-runs
Replies: 32
Views: 7146

Re: expected number of 1-runs

See previous definitions. Looking at probabilities of getting from {a, b, c} to {a, b, c} we get [$]a_{n+1}=c_n+1[$] [$]b_{n+1}=\tfrac{1}{2}b_n+\tfrac{1}{2}(a_n-1)[$] (You lose one 1-run.) [$]c_{n+1}=\tfrac{1}{4}a_n+\tfrac{1}{4}b_n+\tfrac{1}{2}c_n[$] All for [$]n\ge 2[$] (N.b. not true for [$]n=1[$]...
by Paul
May 16th, 2020, 4:53 pm
Forum: Brainteaser Forum
Topic: expected number of 1-runs
Replies: 32
Views: 7146

Re: expected number of 1-runs

That’s because I hate spoon feeding people!

But ok I’ll write it up! (Some of it!)
by Paul
May 15th, 2020, 11:46 pm
Forum: Brainteaser Forum
Topic: expected number of 1-runs
Replies: 32
Views: 7146

Re: expected number of 1-runs

I'm sure that if I put my mind to it I could do it with five variables!
by Paul
May 15th, 2020, 11:30 pm
Forum: Off Topic
Topic: Stupid question of the day
Replies: 2298
Views: 167920

Re: Stupid question of the day

In which language do you?

1. Count
2. Spell letters
3. Swear
4. Pray

Me
Dutch: 2,3
English 1
Latin 4
1. Symbols only, usually Greek alphabet
2. English
3. N/A
4. If/when becomes necessary will let you know
by Paul
May 15th, 2020, 11:12 pm
Forum: Brainteaser Forum
Topic: expected number of 1-runs
Replies: 32
Views: 7146

Re: expected number of 1-runs

There might be an easier way, but this is my classical, albeit a bit tedious, way. The trick is to figure out what variables you need to keep track of the kind of path dependency that's in this. I used [$]a_n=\mbox{ Expected number of 1 runs when sequence ends on H and is a 1 run}[$], i.e. second to...
by Paul
May 15th, 2020, 10:56 pm
Forum: Brainteaser Forum
Topic: expected number of 1-runs
Replies: 32
Views: 7146

Re: expected number of 1-runs

I'd give you my solution but I'm afraid of all the accolades...
GZIP: On