Guy Melançon - Enseignement

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#	Time	Memory	Function	Location
1	0.0003	400736	{main}( )	.../doku.php:0
2	0.2209	1462408	act_dispatch( )	.../doku.php:124
3	0.2223	1464960	include( '/net/www/gmelanco/dokuwiki/lib/tpl/dokuwiki/main.php' )	.../actions.php:199
4	0.2309	1470888	tpl_content( )	.../main.php:59
5	0.2309	1487400	trigger_event( )	.../template.php:83
6	0.2309	1487560	Doku_Event->trigger( )	.../events.php:238
7	0.2309	1487560	tpl_content_core( )	.../events.php:111
8	0.2310	1487560	html_diff( )	.../template.php:129
9	0.2572	1595472	p_locale_xhtml( )	.../html.php:1349
10	0.2573	1595552	p_cached_output( )	.../parserutils.php:103
11	0.2587	1597432	p_cached_instructions( )	.../parserutils.php:128
12	0.2620	1598952	p_get_instructions( )	.../parserutils.php:167
13	0.2624	1237184	Doku_Parser->parse( )	.../parserutils.php:205
14	0.3119	1585896	Doku_Lexer->parse( )	.../parser.php:120
15	0.3119	1585920	Doku_Lexer->_reduce( )	.../lexer.php:407
16	0.3119	1585944	Doku_LexerParallelRegex->split( )	.../lexer.php:553
17	0.3182	1600272	preg_match ( )	.../lexer.php:118

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--- miage_solution:solution_kodja_markov_2_etats [2017/01/08 19:41]
melancon created
+++ miage_solution:solution_kodja_markov_2_etats [2018/01/21 20:13] (current)
melancon
@@ Line 1: / Line 1: @@
-=== Exercice ===
+====== Master 4TYE814U/4TYE808U MIAGE & e-MIAGE  -- Processus stochastiques et simulation ======
+===== Séance de travaux dirigé =====
+==== Exercice ====
 On revient à la chaîne de Markov à deux états de la section précédente.
@@ Line 9: / Line 15: @@
 $$
+----
 On reprend la définition de la probabilité conditionnelle:
 $$
-P(X_1 = 0 | X_0 = 0, X_2 = 0) = \frac{P(X_1 = 0 \& X_0 = 0 \& X_2 = 0)}{P(X_0 = 0 \& X_2 = 0)}
+P(X_1 = 0 | X_0 = 0, X_2 = 0) = \frac{P(X_1 = 0 \cap X_0 = 0 \cap X_2 = 0)}{P(X_0 = 0 \cap X_2 = 0)}
 $$
@@ Line 19: / Line 26: @@
 $$
-P(X_0 = 0 \& X_2 = 0) = P(X_0 = 0 \& X_1 = 0 \& X_2 = 0) + P(X_0 = 0 \& X_1 = 1 \& X_2 = 0)
+P(X_0 = 0 \cap X_2 = 0) = P(X_0 = 0 \cap X_1 = 0 \cap X_2 = 0) + P(X_0 = 0 \cap X_1 = 1 \cap X_2 = 0)
 $$
@@ Line 25: / Line 32: @@
 $$
-P(X_1 = 0 | X_0 = 0, X_2 = 0) = \frac{P(X_1 = 0 \& X_0 = 0 \& X_2 = 0)}{P(X_0 = 0 \& X_1 = 0 \& X_2 = 0) + P(X_0 = 0 \& X_1 = 1 \& X_2 = 0)}
+P(X_1 = 0 | X_0 = 0, X_2 = 0) = \frac{P(X_1 = 0 \cap X_0 = 0 \cap X_2 = 0)}{P(X_0 = 0 \cap X_1 = 0 \cap X_2 = 0) + P(X_0 = 0 \cap X_1 = 1 \cap X_2 = 0)}
 $$
@@ Line 31: / Line 38: @@
 $$
-P(X_2 = 0 \& X_1 = 0 \& X_0 = 0) = P(X_2 = 0 | X_1 = 0) P(X_1 = 0 | X_0 = 0) P(X_0 = 0)
+P(X_2 = 0 \cap X_1 = 0 \cap X_0 = 0) = P(X_2 = 0 | X_1 = 0) P(X_1 = 0 | X_0 = 0) P(X_0 = 0)
 $$
 $$
-P(X_2 = 0 \& X_0 = 1 \& X_0 = 0) = P(X_2 = 0 | X_1 = 1) P(X_1 = 1 | X_0 = 0) P(X_0 = 0)
+P(X_2 = 0 \cap X_0 = 1 \cap X_0 = 0) = P(X_2 = 0 | X_1 = 1) P(X_1 = 1 | X_0 = 0) P(X_0 = 0)
 $$
@@ Line 56: / Line 63: @@
 [[miage:td_analytique|Retourner au TD]]

( ! ) Warning: Declaration of action_plugin_divalign2::register(&$controller) should be compatible with DokuWiki_Action_Plugin::register(Doku_Event_Handler $controller) in /net/www/gmelanco/dokuwiki/lib/plugins/divalign2/action.php on line 0
Call Stack
#	Time	Memory	Function	Location
1	0.0003	400736	{main}( )	.../doku.php:0
2	0.0015	402096	require_once( '/net/www/gmelanco/dokuwiki/inc/init.php' )	.../doku.php:34
3	0.0378	480704	Doku_Event_Handler->__construct( )	.../init.php:216
4	0.0438	572088	plugin_load( )	.../events.php:164
5	0.0438	572088	Doku_Plugin_Controller->load( )	.../pluginutils.php:45
6	0.0438	572136	class_exists ( )	.../plugincontroller.class.php:95
7	0.0438	572136	spl_autoload_call ( )	.../plugincontroller.class.php:95
8	0.0439	572136	load_autoload( )	.../plugincontroller.class.php:95

( ! ) Warning: Declaration of syntax_plugin_divalign2_common::handle($match, $state, $pos, &$handler) should be compatible with DokuWiki_Syntax_Plugin::handle($match, $state, $pos, Doku_Handler $handler) in /net/www/gmelanco/dokuwiki/lib/plugins/divalign2/common.php on line 28
Call Stack
#	Time	Memory	Function	Location
1	0.0003	400736	{main}( )	.../doku.php:0
2	0.0015	402096	require_once( '/net/www/gmelanco/dokuwiki/inc/init.php' )	.../doku.php:34
3	0.0378	480704	Doku_Event_Handler->__construct( )	.../init.php:216
4	0.0438	572088	plugin_load( )	.../events.php:164
5	0.0438	572088	Doku_Plugin_Controller->load( )	.../pluginutils.php:45
6	0.0438	572136	class_exists ( )	.../plugincontroller.class.php:95
7	0.0438	572136	spl_autoload_call ( )	.../plugincontroller.class.php:95
8	0.0439	572136	load_autoload( )	.../plugincontroller.class.php:95
9	0.0445	574680	require( '/net/www/gmelanco/dokuwiki/lib/plugins/divalign2/action.php' )	.../load.php:140
10	0.0451	575272	require_once( '/net/www/gmelanco/dokuwiki/lib/plugins/divalign2/common.php' )	.../action.php:12

( ! ) Warning: Declaration of syntax_plugin_divalign2_common::render($mode, &$renderer, $data) should be compatible with DokuWiki_Syntax_Plugin::render($format, Doku_Renderer $renderer, $data) in /net/www/gmelanco/dokuwiki/lib/plugins/divalign2/common.php on line 28
Call Stack
#	Time	Memory	Function	Location
1	0.0003	400736	{main}( )	.../doku.php:0
2	0.0015	402096	require_once( '/net/www/gmelanco/dokuwiki/inc/init.php' )	.../doku.php:34
3	0.0378	480704	Doku_Event_Handler->__construct( )	.../init.php:216
4	0.0438	572088	plugin_load( )	.../events.php:164
5	0.0438	572088	Doku_Plugin_Controller->load( )	.../pluginutils.php:45
6	0.0438	572136	class_exists ( )	.../plugincontroller.class.php:95
7	0.0438	572136	spl_autoload_call ( )	.../plugincontroller.class.php:95
8	0.0439	572136	load_autoload( )	.../plugincontroller.class.php:95
9	0.0445	574680	require( '/net/www/gmelanco/dokuwiki/lib/plugins/divalign2/action.php' )	.../load.php:140
10	0.0451	575272	require_once( '/net/www/gmelanco/dokuwiki/lib/plugins/divalign2/common.php' )	.../action.php:12

( ! ) Warning: Cannot modify header information - headers already sent by (output started at /net/www/gmelanco/dokuwiki/lib/plugins/divalign2/common.php:28) in /net/www/gmelanco/dokuwiki/inc/auth.php on line 495
Call Stack
#	Time	Memory	Function	Location
1	0.0003	400736	{main}( )	.../doku.php:0
2	0.0015	402096	require_once( '/net/www/gmelanco/dokuwiki/inc/init.php' )	.../doku.php:34
3	0.0554	737808	auth_setup( )	.../init.php:224
4	0.0575	749664	trigger_event( )	.../auth.php:109
5	0.0575	749824	Doku_Event->trigger( )	.../events.php:238
6	0.0575	749824	auth_login_wrapper( )	.../events.php:111
7	0.0575	749824	auth_login( )	.../auth.php:177
8	0.0576	749848	auth_logoff( )	.../auth.php:265
9	0.0576	749848	setcookie ( )	.../auth.php:495

( ! ) Warning: preg_match(): Compilation failed: invalid range in character class at offset 5073 in /net/www/gmelanco/dokuwiki/inc/parser/lexer.php on line 118
Call Stack
#	Time	Memory	Function	Location
1	0.0003	400736	{main}( )	.../doku.php:0
2	0.0596	753360	pageinfo( )	.../doku.php:91
3	0.0619	756184	p_get_metadata( )	.../common.php:245
4	0.0656	839040	p_render_metadata( )	.../parserutils.php:270
5	0.0656	840000	p_cached_instructions( )	.../parserutils.php:480
6	0.0746	845112	p_get_instructions( )	.../parserutils.php:167
7	0.0966	977640	Doku_Parser->parse( )	.../parserutils.php:205
8	0.1484	1361488	Doku_Lexer->parse( )	.../parser.php:120
9	0.1485	1361512	Doku_Lexer->_reduce( )	.../lexer.php:407
10	0.1485	1361536	Doku_LexerParallelRegex->split( )	.../lexer.php:553
11	0.1549	1375864	preg_match ( )	.../lexer.php:118

Guy Melançon - Enseignement

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