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Uebersetzung

28/03/2010 - 10:03 von Phred Phungus | Report spam
Na newsgroup,

Ich suche hiermit eine Uebersetzung des foldenden:

If U is uniformly distributed on interval [0,M], then U2 will be
distributed on interval [0,M2]. Find the distribution as follows: for
any x in (0,M2) the cumulative distribution of U2 is F(x) = Pr{U2
<= x} = Pr{U <= sqrt(x)}; we don't have negative values of U, so we
don't consider the interval from -sqrt(x) to 0. Anyway, for uniform U
on [0,M], Pr{U <= y} = y/M for y in [0,M]. For y = sqrt(x) this gives
Pr{U2 <= x} = sqrt(x)/M [note: the right-hand-side = 1 when x = M2,
as it should]. Thus, the density function of U2 is f(x) = dF(x)/dx (1/2)/[M*sqrt(x)].

VielenDank.
fred

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#1 gwoegi
28/03/2010 - 15:50 | Warnen spam
Phred Phungus wrote:
# Na newsgroup,
#
# Ich suche hiermit eine Uebersetzung des foldenden:
#
# If U is uniformly distributed on interval [0,M], then U2 will be
# distributed on interval [0,M2]. Find the distribution as follows: for
# any x in (0,M2) the cumulative distribution of U2 is F(x) = Pr{U2
# <= x} = Pr{U <= sqrt(x)}; we don't have negative values of U, so we
# don't consider the interval from -sqrt(x) to 0. Anyway, for uniform U
# on [0,M], Pr{U <= y} = y/M for y in [0,M]. For y = sqrt(x) this gives
# Pr{U2 <= x} = sqrt(x)/M [note: the right-hand-side = 1 when x = M2,
# as it should]. Thus, the density function of U2 is f(x) = dF(x)/dx # (1/2)/[M*sqrt(x)].
#
# VielenDank.
# --
# fred
#

Hast Du die Loesung zu Deiner Hausuebung in einem Englischen
Buch entdeckt, und weisst nun nicht, was das auf Deutsch heisst?

Na, auf jeden Fall sind "U2" und "M2" mit "U^2" und "M^2"
zu uebersetzen...


___________________________________________________________
Gerhard J. Woeginger http://www.win.tue.nl/~gwoegi/

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