vv

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5 years, 237 days

MaplePrimes Activity


These are questions asked by vv

Here is a known probability riddle:

A and B are two lists of 100 binary numbers:

A:=[0,1,0,1,0,1,1,0,1,1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,1,0]:
B:=[0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,1,1,0,0,0,0,0,0,1,0,1,1,1,0,0,0,1,0,1,0,0,0,0,1,0,0,0,0,1,0,1,1,1,1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,1,0]:

One was obtained by tossing a coin (1 for a head, 0 for a tail), and the other by a human, who was asked to simulate tossing a coin.

Question: which one comes from a human brain?
The standard answer: B was produced using a coin, because (among other things) the probabilty of obtaining a "000000" or "111111" is about 80%, but a humain brain tends to avoid such "simulations".

My Question: what (if any) statistical test can be used in Maple for an answer?
(I have tried ChiSquareSuitableModelTest but both lists were accepted).

 

restart;
plot([sin(x), sin(x), x=0..420]);

The matrix A := op([1,1], %)  has equal columns, so the bug is in the PLOT engine.
plot(A) generates the same plot.
See also the "circle":
plot([cos(x), sin(x), x=0..5000*Pi]);

 

combine(2^n*4, icombine);

2^(2+n)

(1)

combine(2^n*4);

4*2^n

(2)

combine(2^n/4, icombine); # BUG

Error, (in compat) invalid input: igcd received undefined, which is not valid for its 2nd argument

 

combine(2^n/4);

(1/4)*2^n

(3)

combine(2^n/2^m, icombine); # BUG

Error, (in compat) invalid input: igcd received undefined, which is not valid for its 2nd argument

 

combine(2^n*2^(-m), icombine);

2^(n-m)

(4)

combine(2^n/2^m);

2^(n-m)

(5)

is(2^n/4 = 2^(n-2)); # ???

false

(6)

 


Download bug-icombine-is.mw

The  plots help page contains an entry for ternaryplot. But it is empty (Maple 2018&2019) and there is no such command.
Does somebody know about it?

searchtext and SearchText do not work well with non-ASCII characters.
Strangely, StringTools:-Search is OK.

restart;
m:=convert([77,97,116,104,195,169,109,97,116,105,113,117,101], bytes);
                      m := "Mathématique"
seq(searchtext(m[i..7], m), i=1..7);
                      1, 0, 0, 4, 0, 0, 1
seq(SearchText(m[i..7], m), i=1..7);
                      1, 0, 0, 4, 0, 0, 7
seq(StringTools:-Search(m[i..7], m), i=1..7);
                      1, 2, 3, 4, 5, 6, 7

 

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