Translate and Scale Normal Distribution
$begingroup$
Working through some problems in Introduction to Probability, Blitzstein.
Let Z ~ N(0,1). Create an r.v. Y ~ N(1,4), as a simple-looking function of Z. Make sure to check that your Y has the correct mean and variance.
Definition of standardization of Normal Function is:
$frac{X-mu}{sigma}$~N(0,1)
Z~N(0,1)
Therefore:
$frac{Y-mu}{sigma}$ ~ Z
$frac{Y-1}{2}$ ~ Z- Y~$2Z+1$
Is that all I'd need to do?
random-variables normal-distribution
asked Dec 3 '18 at 18:49
user603569user603569
728
$endgroup$
add a comment |
$begingroup$
Working through some problems in Introduction to Probability, Blitzstein.
Let Z ~ N(0,1). Create an r.v. Y ~ N(1,4), as a simple-looking function of Z. Make sure to check that your Y has the correct mean and variance.
Definition of standardization of Normal Function is:
$frac{X-mu}{sigma}$~N(0,1)
Z~N(0,1)
Therefore:
$frac{Y-mu}{sigma}$ ~ Z
$frac{Y-1}{2}$ ~ Z- Y~$2Z+1$
Is that all I'd need to do?
random-variables normal-distribution
asked Dec 3 '18 at 18:49
user603569user603569
728
$endgroup$
$begingroup$
Seems okey for me!
$endgroup$
– Ramiro Scorolli
Dec 3 '18 at 18:54
add a comment |
$begingroup$
Working through some problems in Introduction to Probability, Blitzstein.
Let Z ~ N(0,1). Create an r.v. Y ~ N(1,4), as a simple-looking function of Z. Make sure to check that your Y has the correct mean and variance.
Definition of standardization of Normal Function is:
$frac{X-mu}{sigma}$~N(0,1)
Z~N(0,1)
Therefore:
$frac{Y-mu}{sigma}$ ~ Z
$frac{Y-1}{2}$ ~ Z- Y~$2Z+1$
Is that all I'd need to do?
random-variables normal-distribution
asked Dec 3 '18 at 18:49
user603569user603569
728
$endgroup$
Working through some problems in Introduction to Probability, Blitzstein.
Let Z ~ N(0,1). Create an r.v. Y ~ N(1,4), as a simple-looking function of Z. Make sure to check that your Y has the correct mean and variance.
Definition of standardization of Normal Function is:
$frac{X-mu}{sigma}$~N(0,1)
Z~N(0,1)
Therefore:
$frac{Y-mu}{sigma}$ ~ Z
$frac{Y-1}{2}$ ~ Z- Y~$2Z+1$
Is that all I'd need to do?
random-variables normal-distribution
random-variables normal-distribution
asked Dec 3 '18 at 18:49
user603569user603569
728
asked Dec 3 '18 at 18:49
user603569user603569
728
asked Dec 3 '18 at 18:49
user603569user603569
728
asked Dec 3 '18 at 18:49
user603569user603569
728
asked Dec 3 '18 at 18:49
user603569user603569
728
728
$begingroup$
Seems okey for me!
$endgroup$
– Ramiro Scorolli
Dec 3 '18 at 18:54
add a comment |
$begingroup$
Seems okey for me!
$endgroup$
– Ramiro Scorolli
Dec 3 '18 at 18:54
$begingroup$
Seems okey for me!
$endgroup$
– Ramiro Scorolli
Dec 3 '18 at 18:54
$begingroup$
Seems okey for me!
$endgroup$
– Ramiro Scorolli
Dec 3 '18 at 18:54
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
You also need to verify:
Make sure to check that your Y has the correct mean and variance.
For this, compute mean and variance of $Y$ from given mean and variance of $Z$ using
properties of mean and variance (e.g. linearity in case of mean. What happens in case of variance?).
Relation you have proposed above.
and verify that indeed you get $1$ and $4$.
answered Dec 3 '18 at 19:00
DineshDinesh
461513
$endgroup$
add a comment |
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',
autoActivateHeartbeat: false,
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
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3024505%2ftranslate-and-scale-normal-distribution%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
You also need to verify:
Make sure to check that your Y has the correct mean and variance.
For this, compute mean and variance of $Y$ from given mean and variance of $Z$ using
properties of mean and variance (e.g. linearity in case of mean. What happens in case of variance?).
Relation you have proposed above.
and verify that indeed you get $1$ and $4$.
answered Dec 3 '18 at 19:00
DineshDinesh
461513
$endgroup$
add a comment |
$begingroup$
You also need to verify:
Make sure to check that your Y has the correct mean and variance.
For this, compute mean and variance of $Y$ from given mean and variance of $Z$ using
properties of mean and variance (e.g. linearity in case of mean. What happens in case of variance?).
Relation you have proposed above.
and verify that indeed you get $1$ and $4$.
answered Dec 3 '18 at 19:00
DineshDinesh
461513
$endgroup$
add a comment |
$begingroup$
You also need to verify:
Make sure to check that your Y has the correct mean and variance.
For this, compute mean and variance of $Y$ from given mean and variance of $Z$ using
properties of mean and variance (e.g. linearity in case of mean. What happens in case of variance?).
Relation you have proposed above.
and verify that indeed you get $1$ and $4$.
answered Dec 3 '18 at 19:00
DineshDinesh
461513
$endgroup$
You also need to verify:
Make sure to check that your Y has the correct mean and variance.
For this, compute mean and variance of $Y$ from given mean and variance of $Z$ using
properties of mean and variance (e.g. linearity in case of mean. What happens in case of variance?).
Relation you have proposed above.
and verify that indeed you get $1$ and $4$.
answered Dec 3 '18 at 19:00
DineshDinesh
461513
answered Dec 3 '18 at 19:00
DineshDinesh
461513
answered Dec 3 '18 at 19:00
DineshDinesh
461513
answered Dec 3 '18 at 19:00
DineshDinesh
461513
461513
add a comment |
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3024505%2ftranslate-and-scale-normal-distribution%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
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
$begingroup$
Seems okey for me!
$endgroup$
– Ramiro Scorolli
Dec 3 '18 at 18:54