Latest revision as of 12:00, 22 November 2011

Independence

Two events A and B are independent if the following formula holds:

$P(A \bigcap B) = P(A) \times P(B)$

For example, given a coin, are the two outcomes independent?

$P( \lbrace C_1=H \rbrace \bigcap \lbrace C_2 =H \rbrace ) = 1/4$

$P( C_1=H ) \times P(C_2=H) = 1/2 \times 1/2 = 1/4$

Since the product of the two probabilities is equal to overall probability, the events are independent.

$P( \bigcap_{i \in S} A_i ) = \prod_{i \in S} P(A_i)$ for all sets $$ S $$ of events.

A & B are conditionally independent given C if the following formula holds true.

$P(A \bigcap B|C) = P(A|C) \times P(B|C)$

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-==Independence in Probability==
+[[Category:ECE302Fall2008_ProfSanghavi]]
+[[Category:probabilities]]
+[[Category:ECE302]]
-==Independence in Multiple Events==
+=Independence=
-==Independence in Conditional Probability==
+==In Two Events==
+Two events A and B are independent if the following formula holds:
+<math>P(A \bigcap B) = P(A) \times P(B) </math>
+For example, given a coin, are the two outcomes independent?
+<math> P( \lbrace C_1=H \rbrace  \bigcap  \lbrace C_2 =H \rbrace  ) = 1/4</math>
+<math> P( C_1=H ) \times P(C_2=H) = 1/2 \times 1/2 = 1/4</math>
+Since the product of the two probabilities is equal to overall probability, the events are independent.
+[http://en.wikipedia.org/wiki/Help:Formula]
+==In Multiple Events==
+<math> P( \bigcap_{i \in S} A_i ) = \prod_{i \in S} P(A_i)</math> for all sets <math> S </math> of events.
+==Conditional Probability==
+A & B are conditionally independent given C if the following formula holds true.
+<math>P(A \bigcap B|C) = P(A|C) \times P(B|C)</math>
+----
+[[Main_Page_ECE302Fall2008sanghavi|Back to ECE302 Fall 2008 Prof. Sanghavi]]