Kamandirian statistik: Béda antarrépisi
Konten dihapus Konten ditambahkan
Addbot (obrolan | kontribusi) m Bot: Migrating 25 interwiki links, now provided by Wikidata on d:q625303 (translate me) |
m Ngarapihkeun éjahan, replaced: rea → réa (3), ngarupakeun → mangrupa (2), yen → yén (3) using AWB |
||
Baris ka-1:
{{tarjamahkeun|Inggris}}
Dina [[tiori probabiliti]], keur nyebutkeun
Hal nu sarupa, waktu urang nyebutkeun dua [[variabel acak]] bebas, we intuitively mean that knowing something about the value of one of them does not yield any information about the value of the other. For example, the number appearing on the upward face of a die the first time it is thrown and that appearing the second time are independent.
Baris ka-10:
:<math>P(A\mid B)=P(A).</math>
There are at least two
When one recalls that the conditional probability P(''A'' | ''B'') is given by
Baris ka-26:
:Two events ''A'' and ''B'' are '''independent''' [[iff]] P(''A'' ∩ ''B'')=P(''A'')P(''B'').
More generally, and collection of
:<math>P(A_1 \cap \cdots \cap A_n)=P(A_1)\,\cdots\,P(A_n).</math>
Baris ka-36:
== Independent random variables ==
Two random variables ''X'' and ''Y'' are independent iff for any numbers ''a'' and ''b'' the events [''X'' ≤ ''a''] and [''Y'' ∈ ''b''] are independent events as defined above. Similarly an arbitrary collection of random
The measure-theoretically inclined may prefer to substitute events [''X'' ∈ ''A''] for events [''X'' ≤ ''a''] in the above definition, where ''A'' is any [[Borel algebra|Borel set]]. That definition is exactly equivalant to the one above when the values of the random variables are [[real number]]s. It has the advantage of working also for complex-valued random variables or for random variables taking values in any [[topological space]].
Lamun ''X'' sarta ''Y'' bebas, mangka [[nilai ekspektasi|operator ekspektasi]] ''E'' mibanda sipat nu hade
:E[''X''· ''Y''] = E[''X''] · E[''Y'']
Baris ka-52:
:var(''X'' + ''Y'') = var(''X'') + var(''Y'') + 2 cov(''X'', ''Y'').
(''Pernyataan'' sabalikna
Furthermore, if ''X'' and ''Y'' are independent and have [[probability density function|probability densities]] ''f''<sub>''X''</sub>(''x'') and ''f''<sub>''Y''</sub>(''y''), then the combined random variable (''X'',''Y'') has a joint density
Baris ka-63:
: P[(''X'' in ''A'') & (''Y'' in ''B'') | ''Z'' in ''C''] = P[''X'' in ''A'' | ''Z'' in ''C''] · P[''Y'' in ''B'' | ''Z'' in ''C'']
for any Borel subsets ''A'', ''B'' and ''C'' of the
If ''X'' and ''Y'' are conditionally independent given ''Z'', then
: P[(''X'' in ''A'') | (''Y'' in ''B'') & (''Z'' in ''C'')]
:= P[(''X'' in ''A'') | (''Z'' in ''C'')]
for any Borel subsets ''A'', ''B'' and ''C'' of the
Independence can be seen as a special kind of conditional independence, since probability can be seen as a kind of conditional probability given no events.
| |||