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manuel1109
science forum beginner


Joined: 21 Nov 2005
Posts: 3

PostPosted: Mon Nov 21, 2005 4:03 am    Post subject: Re: Does poker betting exaggerate skill differences? Reply with quote

I believe the roulette example is commonly known as the Gambler's Dilema.
http://www.everything2.com/index.pl?node=the%20gambler%27s%20dilemma

As for the poker example I would suppose that having the cushion of money
is the major benefit, and that you are right, someone who has little skill
at bluffing and counting hands would benefit from a quick game.

On Thu, 20 Oct 2005 01:15:42 -0400, Mark Spahn wrote:

Quote:

"Pavel314" <Pavel314@NOSPAM.comcast.net> wrote in message news:WMSdndCwYeeqY8veRVn-sg@comcast.com...
Mark Spahn" <mspahn@localnet.com> wrote in message news:11l6nr3et21lnb2@corp.supernews.com...
Suppose five friends A, B, C, D, E have a weekly evening
of poker in which they each start with $10 and play until
one player has won all the money (a gain of $40).
Their skills differ so that their respective probabilities of
winning a hand of poker are .22, .21, .20, .19, .18.
Are their probabilities of winning for the evening (= 20 hands;
is that a reasonable number?) identical to their probabilities
of winning a hand?
During the course of a poker evening, as one player gains
more money than the others, does his having more money
to bet confer an advantage, so his probability of winning
for the evening rises? If so, then the players' probabilities
of winning an evening of poker might be, say,
.24, .22, .20, .18, .16.
Can anyone shed some light on this question?

-- Mark Spahn

Mark,

I wrote a program in Ubasic to simulate the five friends playing poker. The program simulated 10,000 weekly games or 192.3 years. The program assumes the same bet on each hand. When a player loses all his money, he's out of the game and the others play on. When the final player has the entire $50, the game is over. Higher skill on the per-hand level definitely leverages your odds at the evening game level.

RESULTS

Player Win
Probability____$1 Bet__________$5 Bet_______$10 Bet

.18 1.47% 5.86% 17.95%
.19 5.32% 10.60% 18.70%
.20 13.11% 17.82% 20.45%
.21 29.25% 27.99% 20.86%
.22 50.85% 37.73% 22.04%

In my earlier reply to your problem, I said that I expected the less skilled players to have better odds with larger bets but I never expected the disproportionate results on the $1 bet games. It seems that over the long haul, skill gives you the ability to build up the cash cushion which helps you survive runs of bad luck later in the game.

Just as a test, I set everyone at the same skill level. Even at the $1 bet level the results are fairly even, which increases my confidence in my simulation program.

Player Win
Probability____$1 Bet

.20 19.92%
.20 20.48%
.20 19.73%
.20 20.07%
.20 19.80%


Finally, I let four players have equal skill level and set the fifth at a significantly higher level. The results are as you might expect:

Player Win
Probability____$1 Bet

.18 2.98%
.18 3.12%
.18 2.69%
.18 3.15%
.28 88.06%

The moral is that if you're against better opponents, put everything on one test and trust to luck; if you are the most skilled, try to draw the contest out to bring your skill into play.

E.G., in roulette the house is the more "skilled" player by virtue of having the odds in its favor, I believe 52% for the house to 48% for the player. So put all your chips on one roll and cross your fingers.

Any suggestions on how to apply this lesson to the stock market?

Paul

Paul,
Wow, bravo! I am impressed, and just as surprised as you at how much the ability to accumulate a bankroll magnifies the hand-winning probability into a much larger game-winning probability. I remember reading somewhere that Richard Nixon, when he learned poker while in the navy, observed and studied many, many games before he actually began to bet money. It looks like that was a good plan, because the skill of a neophyte player, even if only slightly below par, will be decisively overwhelmed by the better skill of the other players.
-- Mark
!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"
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DIV><FONT face="Times New Roman"></FONT>&nbsp;</DIV
BLOCKQUOTE dir=ltr
style="PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px"
DIV>"Pavel314" <<A
href="mailto:Pavel314@NOSPAM.comcast.net">Pavel314@NOSPAM.comcast.net</A
wrote in message <A
href="news:WMSdndCwYeeqY8veRVn-sg@comcast.com">news:WMSdndCwYeeqY8veRVn-sg@comcast.com</A>...</DIV
DIV>Mark Spahn" <<A
href="mailto:mspahn@localnet.com">mspahn@localnet.com</A>> wrote in message
A
href="news:11l6nr3et21lnb2@corp.supernews.com">news:11l6nr3et21lnb2@corp.supernews.com</A>...</DIV
BLOCKQUOTE dir=ltr
style="PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px"
DIV><FONT face="Times New Roman">Suppose five friends A, B, C, D, E have a
weekly evening</FONT></DIV
DIV><FONT face="Times New Roman">of poker in which they each start with
$10&nbsp;and play until</FONT></DIV
DIV><FONT face="Times New Roman">one player has won all the money (a gain
of $40).</FONT></DIV
DIV><FONT face="Times New Roman">Their skills differ so that their
respective probabilities of</FONT></DIV
DIV><FONT face="Times New Roman">winning a hand of poker are .22, .21, .20,
.19, .18.</FONT></DIV
DIV><FONT face="Times New Roman">Are their probabilities of winning for the
evening (= 20 hands;</FONT></DIV
DIV><FONT face="Times New Roman">is that a reasonable number?) identical
/FONT><FONT face="Times New Roman">to their probabilities </FONT></DIV
DIV><FONT face="Times New Roman">of winning a hand?</FONT></DIV
DIV><FONT face="Times New Roman">During the course of a poker evening, as
one player gains</FONT></DIV
DIV><FONT face="Times New Roman">more money than the others, does his
having more money</FONT></DIV
DIV><FONT face="Times New Roman">to bet confer an advantage, so his
probability of winning</FONT></DIV
DIV><FONT face="Times New Roman">for the evening rises?&nbsp; If so, then
the players' probabilities</FONT></DIV
DIV><FONT face="Times New Roman">of winning an evening of poker might be,
say,</FONT></DIV
DIV><FONT face="Times New Roman">.24, .22, .20, .18, .16.</FONT></DIV
DIV><FONT face="Times New Roman">Can anyone shed some light on this
question?</FONT></DIV
DIV><FONT face="Times New Roman"></FONT>&nbsp;</DIV
DIV><FONT face="Times New Roman">-- Mark Spahn</FONT></DIV></BLOCKQUOTE
DIV dir=ltr><FONT face="Times New Roman"></FONT>&nbsp;</DIV
DIV dir=ltr><FONT face="Times New Roman">Mark,</FONT></DIV
DIV dir=ltr><FONT face="Times New Roman"></FONT>&nbsp;</DIV
DIV dir=ltr><FONT face="Times New Roman">I wrote a program in Ubasic to
simulate the five friends playing poker. The program simulated 10,000 weekly
games or 192.3 years. The program assumes the same bet on each hand. When a
player loses all his money, he's out of the game and the others play on. When
the final player has the entire $50, the game is over. Higher skill on the
per-hand level definitely&nbsp;leverages&nbsp;your odds at the&nbsp;evening
game level.&nbsp;</FONT></DIV
DIV dir=ltr><FONT face="Times New Roman"></FONT><FONT
face="Times New Roman"></FONT>&nbsp;</DIV
DIV dir=ltr><FONT face="Times New Roman">RESULTS</FONT></DIV
DIV dir=ltr><FONT face="Times New Roman"></FONT>&nbsp;</DIV
DIV dir=ltr><FONT face="Times New Roman">Player Win&nbsp;</FONT></DIV
DIV dir=ltr><FONT face="Times New Roman">Probability____$1 Bet__________$5
Bet_______$10 Bet</FONT></DIV
DIV dir=ltr><FONT face="Times New Roman"></FONT>&nbsp;</DIV
DIV dir=ltr><FONT
face="Times New Roman">.18&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1.47%&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
5.86%&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
17.95%</FONT></DIV
DIV dir=ltr><FONT
face="Times New Roman">.19&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
5.32%&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;10.60%&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
18.70%&nbsp;</FONT></DIV
DIV dir=ltr><FONT
face="Times New Roman">.20&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;13.11%&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
17.82%&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
20.45%</FONT></DIV
DIV dir=ltr><FONT
face="Times New Roman">.21&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
29.25%&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;27.99%&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
20.86%&nbsp; &nbsp;</FONT></DIV
DIV dir=ltr><FONT
face="Times New Roman">.22&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
50.85%&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
37.73%&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
22.04%</FONT></DIV
DIV dir=ltr><FONT face="Times New Roman"></FONT>&nbsp;</DIV
DIV dir=ltr><FONT face="Times New Roman">In my earlier reply to your problem,
I said that I expected the less skilled players to have better odds with
larger bets but I never expected the disproportionate results on the $1 bet
games. It seems that over the long haul, skill gives you the ability to build
up the cash cushion which helps you survive runs of bad luck later in the
game.</FONT></DIV
DIV dir=ltr><FONT face="Times New Roman"></FONT>&nbsp;</DIV
DIV dir=ltr><FONT face="Times New Roman">Just as a test, I set everyone at
the same skill level. Even at the $1 bet level the results are fairly even,
which increases my confidence in my simulation program.</FONT></DIV
DIV dir=ltr><FONT face="Times New Roman"></FONT>&nbsp;</DIV
DIV dir=ltr
DIV dir=ltr><FONT face="Times New Roman">Player Win&nbsp;</FONT></DIV
DIV dir=ltr><FONT face="Times New Roman">Probability____$1 Bet</FONT></DIV
DIV dir=ltr><FONT face="Times New Roman"></FONT>&nbsp;</DIV
DIV dir=ltr><FONT
face="Times New Roman">.20&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
19.92%&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
/FONT></DIV
DIV dir=ltr><FONT
face="Times New Roman">.20&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
20.48%&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</FONT></DIV
DIV dir=ltr><FONT
face="Times New Roman">.20&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
19.73%&nbsp;</FONT></DIV
DIV dir=ltr><FONT
face="Times New Roman">.20&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
20.07%&nbsp;</FONT></DIV
DIV dir=ltr><FONT
face="Times New Roman">.20&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
19.80%&nbsp;</FONT></DIV
DIV dir=ltr><FONT face="Times New Roman"></FONT>&nbsp;</DIV
DIV dir=ltr><FONT face="Times New Roman"></FONT>&nbsp;</DIV
DIV dir=ltr><FONT face="Times New Roman">Finally, I let four players have
equal skill level and set the fifth at a significantly higher level. The
results are as you might expect:</FONT></DIV
DIV dir=ltr><FONT face="Times New Roman"></FONT>&nbsp;</DIV
DIV dir=ltr><FONT face="Times New Roman"
DIV dir=ltr><FONT face="Times New Roman">Player Win&nbsp;</FONT></DIV
DIV dir=ltr><FONT face="Times New Roman">Probability____$1 Bet</FONT></DIV
DIV dir=ltr><FONT face="Times New Roman"></FONT>&nbsp;</DIV
DIV dir=ltr><FONT
face="Times New Roman">.18&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;2.98%&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
/FONT></DIV
DIV dir=ltr><FONT
face="Times New Roman">.18&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;3.12%&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</FONT></DIV
DIV dir=ltr><FONT
face="Times New Roman">.18&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;2.69%&nbsp;</FONT></DIV
DIV dir=ltr><FONT
face="Times New Roman">.18&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;3.15%&nbsp;</FONT></DIV
DIV dir=ltr><FONT
face="Times New Roman">.28&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
&nbsp;&nbsp;88.06%&nbsp;</FONT></DIV
DIV dir=ltr>&nbsp;</DIV
DIV dir=ltr><FONT face=Arial size=2>The moral is that if you're against
better opponents, put everything on one test and trust to luck; if you are the
most skilled, try to draw the contest out to bring your skill into
play.</FONT></DIV
DIV dir=ltr><FONT face=Arial size=2></FONT>&nbsp;</DIV
DIV dir=ltr><FONT face=Arial size=2>E.G., in roulette the house is the more
"skilled" player by virtue of having the odds in its favor, I believe 52% for
the house to 48% for the player. So put all your chips on one roll and cross
your fingers. </FONT></DIV
DIV dir=ltr><FONT face=Arial size=2></FONT>&nbsp;</DIV
DIV dir=ltr><FONT face=Arial size=2>Any suggestions on how to apply this
lesson to the stock market?</FONT></DIV
DIV dir=ltr><FONT face=Arial size=2></FONT>&nbsp;</DIV
DIV dir=ltr><FONT face=Arial size=2>Paul</FONT></DIV
DIV dir=ltr>&nbsp;</DIV
DIV dir=ltr><FONT face=Arial size=2>Paul,</FONT></DIV
DIV dir=ltr><FONT face=Arial size=2>Wow, bravo!&nbsp; I am impressed, and
just as&nbsp;surprised as you at how much the ability to accumulate a bankroll
magnifies the hand-winning probability into a much larger game-winning
probability.&nbsp; I remember reading somewhere that Richard Nixon, when he
learned poker while in the navy, observed and studied many, many games before
he actually began to bet money.&nbsp; It looks&nbsp;like that&nbsp;was a good
plan, because the skill of a&nbsp;neophyte player, even if only slightly below
par, will be decisively overwhelmed by the better skill of the other
players.</FONT></DIV
DIV dir=ltr><FONT face=Arial size=2>-- Mark</FONT></DIV
DIV dir=ltr><FONT face=Arial
size=2>&nbsp;&nbsp;</FONT></DIV></FONT></DIV></DIV></BLOCKQUOTE></BODY></HTML



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Javriol
science forum beginner


Joined: 16 Jan 2006
Posts: 1

PostPosted: Mon Jan 16, 2006 5:48 pm    Post subject: Re: Probability and Spontaneous Proteins Reply with quote

Elmer wrote:
Quote:
Tudman Todmorden wrote:

(snip)
But any event that
has one chance in just 1050 is dismissed by mathematicians as
never happening.
(snip)

Bull. Please name any mathematician who claims this.

1/10^1050 does not, will not, and never will, equal zero.


ask any..
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Elmer
science forum beginner


Joined: 16 Jan 2006
Posts: 7

PostPosted: Mon Jan 16, 2006 9:51 pm    Post subject: Re: Probability and Spontaneous Proteins Reply with quote

Javriol wrote:
Quote:
Elmer wrote:
Tudman Todmorden wrote:

(snip)
But any event that
has one chance in just 1050 is dismissed by mathematicians as
never happening.
(snip)

Bull. Please name any mathematician who claims this.
1/10^1050 does not, will not, and never will, equal zero.

ask any..

What? Ask any mathematician and they will not say this. This is simply a
lie. There is no way that

1/10^1050 = 0

It does not.
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Greg Heath
science forum beginner


Joined: 24 Feb 2005
Posts: 14

PostPosted: Fri Jun 09, 2006 1:46 pm    Post subject: Re: Normal distribution function with skew and kurtosis Reply with quote

Phil Sherrod wrote:
Quote:
The probability density function for the normal distribution with mean 'm'
and standard deviation 's' is:

1/(s*sqrt(2*Pi)) * exp(-(X-m)^2 / 2s^2)

How can this formula be generalized to include skew and kurtosis?

Go to Google Groups and search on

johnson-transformations

Hope this helps.

Greg
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Konrad Viltersten
science forum addict


Joined: 27 Jun 2005
Posts: 79

PostPosted: Sat Jul 01, 2006 5:45 am    Post subject: Re: Are those variances equal? Reply with quote

Quote:
Suppose you start off with this expression.
V[W_t / t^2]
and you wish to show that it tends towards 0 as t->oo.

What we tried is this rephrasal.
(1/t) * V[W_t / t]
Does it hold?

And then, is it possible to use the fact that
lim t->oo (W_t / t) = 0 (a.s.)
and do a rewriting as follows?

lim t->oo (V[W_t / t]) = V[lim t->oo (W_t / t)]

1. V(a W_t) = a^2 V(W_t) for any scalar a.

True, but how does it work if we have a process, let's
say a Wiener process like {W_t/t}_t>=0. Is it still OK
to regard the t as a scalar? I'd say so, because it's a
deterministic value but i'm a little unsure...

Quote:
2. Convergence a.s. cannot be converted to convergence in variance
without some kind of "dominated convergence."


Allright, i take that as a "definitely maybe". I'll look into
what condition i have and hopefully something will pop-up.

Thank you.

--
Všnligen
Konrad
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as a substitute for coffee

Ambition - a poor excuse for not having
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