Probability econometrics











up vote
0
down vote

favorite












Solve let B distributed as N (0,I) and consider the linear transformations Y= b + BX, where b is a vector and B a k×n matrix of constants, and Z=c+CX where c is an m×1 vector and C an m×n matrix of constants. Show that Y and Z are independent if and only if BC' =0 solutions










share|cite|improve this question
























  • Welcome to MSE! In order to get the best possible answers, it is helpful if you say in what context you encountered the problem, and what your thoughts on it are; this will prevent people from telling you things you already know, and help them give their answers at the right level. Also, many find the use of imperative ("Prove", "Solve", etc.) to be rude when asking for help; please consider rewriting your post.
    – Sambo
    Nov 18 at 14:32















up vote
0
down vote

favorite












Solve let B distributed as N (0,I) and consider the linear transformations Y= b + BX, where b is a vector and B a k×n matrix of constants, and Z=c+CX where c is an m×1 vector and C an m×n matrix of constants. Show that Y and Z are independent if and only if BC' =0 solutions










share|cite|improve this question
























  • Welcome to MSE! In order to get the best possible answers, it is helpful if you say in what context you encountered the problem, and what your thoughts on it are; this will prevent people from telling you things you already know, and help them give their answers at the right level. Also, many find the use of imperative ("Prove", "Solve", etc.) to be rude when asking for help; please consider rewriting your post.
    – Sambo
    Nov 18 at 14:32













up vote
0
down vote

favorite









up vote
0
down vote

favorite











Solve let B distributed as N (0,I) and consider the linear transformations Y= b + BX, where b is a vector and B a k×n matrix of constants, and Z=c+CX where c is an m×1 vector and C an m×n matrix of constants. Show that Y and Z are independent if and only if BC' =0 solutions










share|cite|improve this question















Solve let B distributed as N (0,I) and consider the linear transformations Y= b + BX, where b is a vector and B a k×n matrix of constants, and Z=c+CX where c is an m×1 vector and C an m×n matrix of constants. Show that Y and Z are independent if and only if BC' =0 solutions







normal-distribution






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Nov 18 at 20:02

























asked Nov 18 at 14:15









Nchimunya Moyo

11




11












  • Welcome to MSE! In order to get the best possible answers, it is helpful if you say in what context you encountered the problem, and what your thoughts on it are; this will prevent people from telling you things you already know, and help them give their answers at the right level. Also, many find the use of imperative ("Prove", "Solve", etc.) to be rude when asking for help; please consider rewriting your post.
    – Sambo
    Nov 18 at 14:32


















  • Welcome to MSE! In order to get the best possible answers, it is helpful if you say in what context you encountered the problem, and what your thoughts on it are; this will prevent people from telling you things you already know, and help them give their answers at the right level. Also, many find the use of imperative ("Prove", "Solve", etc.) to be rude when asking for help; please consider rewriting your post.
    – Sambo
    Nov 18 at 14:32
















Welcome to MSE! In order to get the best possible answers, it is helpful if you say in what context you encountered the problem, and what your thoughts on it are; this will prevent people from telling you things you already know, and help them give their answers at the right level. Also, many find the use of imperative ("Prove", "Solve", etc.) to be rude when asking for help; please consider rewriting your post.
– Sambo
Nov 18 at 14:32




Welcome to MSE! In order to get the best possible answers, it is helpful if you say in what context you encountered the problem, and what your thoughts on it are; this will prevent people from telling you things you already know, and help them give their answers at the right level. Also, many find the use of imperative ("Prove", "Solve", etc.) to be rude when asking for help; please consider rewriting your post.
– Sambo
Nov 18 at 14:32















active

oldest

votes











Your Answer





StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");

StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);

StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});

function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});


}
});














 

draft saved


draft discarded


















StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3003588%2fprobability-econometrics%23new-answer', 'question_page');
}
);

Post as a guest















Required, but never shown






























active

oldest

votes













active

oldest

votes









active

oldest

votes






active

oldest

votes
















 

draft saved


draft discarded



















































 


draft saved


draft discarded














StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3003588%2fprobability-econometrics%23new-answer', 'question_page');
}
);

Post as a guest















Required, but never shown





















































Required, but never shown














Required, but never shown












Required, but never shown







Required, but never shown

































Required, but never shown














Required, but never shown












Required, but never shown







Required, but never shown







Popular posts from this blog

Quarter-circle Tiles

build a pushdown automaton that recognizes the reverse language of a given pushdown automaton?

Mont Emei