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<h2 class="hd hd-2 unit-title">When entropic quantities are zero</h2>
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<h2 class="hd hd-2 unit-title">Conditional mutual information</h2>
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<h2 class="hd hd-2 unit-title">CQ: Entropic quantities</h2>
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Entropic quantities
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<div class="problem">
<div>
<p>
This is a concept question, provided to check your understanding of the previous lecture video clips. </p>
<p>
Which of the following are true? </p>
<p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div class="choicegroup capa_inputtype" id="inputtype_cq_M2L6_Entropic_quantities_2_1">
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<text>There are non-deterministic variables that yield zero entropy</text>
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<text>Conditional entropy is zero if and only if both variables are deterministic</text>
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<text>Mutual information is zero if and only if the variables are independent</text>
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<text>Conditional mutual information is always at least the mutual information</text>
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<h3 class="hd hd-3 problem-header" id="cq_M2L6_LB_Conditional_mutual_information_and_data_processing_RB-problem-title" aria-describedby="block-v1:MITx+8.371.3x+2T2018+type@problem+block@cq_M2L6_LB_Conditional_mutual_information_and_data_processing_RB-problem-progress" tabindex="-1">
[Conditional mutual information and data processing]
</h3>
<div class="problem-progress" id="block-v1:MITx+8.371.3x+2T2018+type@problem+block@cq_M2L6_LB_Conditional_mutual_information_and_data_processing_RB-problem-progress"></div>
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<p>
This is a concept question, provided to check your understanding of the previous lecture video clips. </p>
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Which of the following are true? </p>
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<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div class="choicegroup capa_inputtype" id="inputtype_cq_M2L6_LB_Conditional_mutual_information_and_data_processing_RB_2_1">
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<text>Conditional mutual information [mathjaxinline]I(X:Y|Z)[/mathjaxinline] is zero if and only if [mathjaxinline]X \rightarrow Y\rightarrow Z[/mathjaxinline] forms a Markov chain</text>
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<text>Mutual information between a message and a decoded message is at most the mutual information between the input and output of the channel</text>
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<text>Given a Markov chain [mathjaxinline]A \rightarrow B \rightarrow C[/mathjaxinline], it is possible that [mathjaxinline]A : C[/mathjaxinline] has more mutual information than [mathjaxinline]A : B[/mathjaxinline]</text>
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<text>Mutual information is always sub-additive</text>
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}
return {'course_static_url': course_static_url,
'jump_to_url': jump_to_url,
'go_to_search': go_to_search,
'get_search_module': get_search_module,
'get_search_module_ficus': get_search_module_ficus,
'get': get,
}
}
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return;
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var vuid = vblock.data('usage-id').split('@');
var vid;
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vuid = vblock.data('usage-id').split(';_')
vid = vuid[5];
}else{
vid = vuid[2];
}
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var mfnid = mfnpre; // no periods
mfnpre = mfnpre.replace('8_370', '8.370'); // periods in gh filename
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var mke = function(x){ return lb + x + rb; }
var ftid = "fix_transcript_" + mfnid;
if (!$('#' + ftid).length){
var html = lb + "span id='" + ftid + "' style='float:right'" + rb + lb + "a href='#'" + rb;
html += "contribute transcript fix" + mke("/a") + mke("/span");
console.log("html = ", html);
vblock.after(html)
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$('#' + ftid).click(function(){
var cst = $('ol.subtitles').find('li.current');
var cindex = Number(cst.data('index'));
var gurl;
if (mfnpre.endsWith('_cq_sol')){
gurl = "https://github.com/mitocw/content-mit-8370x-cq-sol-subtitles/blob/master/";
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gurl = "https://github.com/mitocw/content-mit-8370x-subtitles/blob/master/";
}
gurl += mfnpre + ".txt#L" + String(cindex + 10 + 1);
console.log("going to ", gurl);
window.open(gurl, "MITx 8.370x subtitle source");
});
});
}
try{
add_fix_transcript();
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var rb = String.fromCharCode(62);
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catch(err){
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<h2 class="hd hd-2 unit-title">Proof of the converse of Shannon's noisy coding theorem - step 2</h2>
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<h3 class="hd hd-2">Proof of the converse of Shannon's noisy coding theorem - step 2</h3>
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var add_site_search = function(){
course_static_url = $('#dummy_course_static_link').attr('href').replace('/NONE', '');
jump_to_url = $('#dummy_jump_link').attr('href').replace('/NONE', '');
if (typeof String.prototype.startsWith != 'function') {
// see below for better implementation!
String.prototype.startsWith = function (str){
return this.indexOf(str) === 0;
};
}
if(typeof(String.prototype.trim) === "undefined")
{
String.prototype.trim = function()
{
return String(this).replace(/^\s+|\s+$/g, '');
};
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var rb = String.fromCharCode(62);
var amp = String.fromCharCode(38);
var rlb = rb + lb;
var mke = function(x){ return lb + x + rb; }
var search_module_url = "";
var get_search_module_ficus = function(){
var cid = $('div.xblock').data('course-id');
if (cid){
console.log("cid = ", cid);
// search_module_url = "/courses/course-v1:MITx+8.371.3x+2T2018/" + cid + "/courseware/welcome/Search_this_course/";
search_module_url = "/courses/course-v1:MITx+8.371.3x+2T2018/courseware/welcome/Search_this_course/"; // automatically rewritten
console.log("3. search_module_url = ", search_module_url);
return;
}
var course_root_link = $('span.nav-item-course').find('a').attr('href');
if (course_root_link){
console.log("course_root_link = ", course_root_link);
search_module_url = course_root_link.replace("course/", "courseware/welcome/Search_this_course/");
console.log("2. search_module_url = ", search_module_url);
return
}
console.log("cannot determine search module url");
}
var get_search_module = function(){
// find search this module link
if (!($('div.course-index').length)){
return get_search_module_ficus();
}
$('div.course-index').find('nav').find('a').each(function(){
if ($(this).text().trim().startsWith("Search this course")){
search_module_url = $(this).attr('href');
console.log("search_module_url = ", search_module_url);
}
});
}
var go_to_search = function(){
get_search_module();
var sterm = $('#site-search-box').val();
// new_url = jump_to_url + "/Search_this_module/?q=" + sterm;
new_url = search_module_url + "?q=" + sterm;
console.log("sterm = ", sterm, " ; going to ", new_url);
window.location.href = new_url;
}
if (!$('#site-search-box').length){
$("nav.courseware").find("ol").append(lb + "section style='float:right'" + rlb + "input size='20'"
+ " id='site-search-box'"
+ rlb + "img src='" + course_static_url
+ "/images_search_glass.png'/" + rlb + "/input" + rlb + "/section" + rb);
}
$("#site-search-box").keypress(function(event) {
if (event.which == 13) {
event.preventDefault();
go_to_search();
}
});
// $('#site-search-box').bind("enterKey", go_to_search);
var get = function(x){
return eval(x);
}
return {'course_static_url': course_static_url,
'jump_to_url': jump_to_url,
'go_to_search': go_to_search,
'get_search_module': get_search_module,
'get_search_module_ficus': get_search_module_ficus,
'get': get,
}
}
var the_site_search = add_site_search();
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return;
}
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var vid;
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vuid = vblock.data('usage-id').split(';_')
vid = vuid[5];
}else{
vid = vuid[2];
}
var mfnpre = vid.split("_video",1)[0];
var mfnid = mfnpre; // no periods
mfnpre = mfnpre.replace('8_370', '8.370'); // periods in gh filename
var lb = String.fromCharCode(60);
var rb = String.fromCharCode(62);
var mke = function(x){ return lb + x + rb; }
var ftid = "fix_transcript_" + mfnid;
if (!$('#' + ftid).length){
var html = lb + "span id='" + ftid + "' style='float:right'" + rb + lb + "a href='#'" + rb;
html += "contribute transcript fix" + mke("/a") + mke("/span");
console.log("html = ", html);
vblock.after(html)
}
$('#' + ftid).click(function(){
var cst = $('ol.subtitles').find('li.current');
var cindex = Number(cst.data('index'));
var gurl;
if (mfnpre.endsWith('_cq_sol')){
gurl = "https://github.com/mitocw/content-mit-8370x-cq-sol-subtitles/blob/master/";
}else{
gurl = "https://github.com/mitocw/content-mit-8370x-subtitles/blob/master/";
}
gurl += mfnpre + ".txt#L" + String(cindex + 10 + 1);
console.log("going to ", gurl);
window.open(gurl, "MITx 8.370x subtitle source");
});
});
}
try{
add_fix_transcript();
}
catch(err){
console.log(err);
}
try{
var rb = String.fromCharCode(62);
setTimeout(function(){ $('.math' + rb + 'span').css("border-left-color","transparent"); }, 3000);
setTimeout(function(){ $('.math' + rb + 'span').css("border-left-color","transparent"); }, 8000);
}
catch(err){
console.log(err);
}
</script></span>
</div>
</div>
</div>
</div>
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