Mixing
Calculating histogram function, $h_X(75.5)$ and $int_{54.2}^{67.8} h_X(x)$
$begingroup$
A population $prod$ and a measure $X$ on $prod$ produced the data set below
$71, 80, 58, 60, 63, 64, 51, 55, 48, 67$
Let $h_X$ denote the density histogram function of $X$ based on the four intervals
$(47, 54.2], (54.2, 63.4], (63.4, 67.8]$ and $(67.8, 81]$
$(a)$ Calculate $h_X(75.5)$
$(b)$ Calculate $int_{54.2}^{67.8} h_X(x) dx$
attempt
$(a)$ I made a table
begin{array}{|c|c|c|c|}
hline
interval& (47, 54.2] & (54.2, 63.4] & (63.4, 67.8] & (67.8, 81] \ hline
frequency & 2/10& 4/10& 2/10 & 2/10\ hline
length & 7.2 & 9.2 & 4.4 & 13.2\ hline
h_X(x) & frac{0.2}{7.2} & frac{0.4}{9.2} & frac{0.2}{4.4} & frac{0.2}{13.2} \ hline
end{array}
Therefore $h_X(75.5)$ lies in $(67.8, 81]$
$h_X(75.5) = frac{0.2}{13.2}$
(b)
$int_{54.2}^{67.8} h_X(x) = F_X(67.8) - F_X(54.2) = frac{8}{10} - frac{2}{10} = frac{6}{10}$
is this correct?
statistics
asked Jan 30 at 20:04
Bas basBas bas
49512
$endgroup$
add a comment |
$begingroup$
A population $prod$ and a measure $X$ on $prod$ produced the data set below
$71, 80, 58, 60, 63, 64, 51, 55, 48, 67$
Let $h_X$ denote the density histogram function of $X$ based on the four intervals
$(47, 54.2], (54.2, 63.4], (63.4, 67.8]$ and $(67.8, 81]$
$(a)$ Calculate $h_X(75.5)$
$(b)$ Calculate $int_{54.2}^{67.8} h_X(x) dx$
attempt
$(a)$ I made a table
begin{array}{|c|c|c|c|}
hline
interval& (47, 54.2] & (54.2, 63.4] & (63.4, 67.8] & (67.8, 81] \ hline
frequency & 2/10& 4/10& 2/10 & 2/10\ hline
length & 7.2 & 9.2 & 4.4 & 13.2\ hline
h_X(x) & frac{0.2}{7.2} & frac{0.4}{9.2} & frac{0.2}{4.4} & frac{0.2}{13.2} \ hline
end{array}
Therefore $h_X(75.5)$ lies in $(67.8, 81]$
$h_X(75.5) = frac{0.2}{13.2}$
(b)
$int_{54.2}^{67.8} h_X(x) = F_X(67.8) - F_X(54.2) = frac{8}{10} - frac{2}{10} = frac{6}{10}$
is this correct?
statistics
asked Jan 30 at 20:04
Bas basBas bas
49512
$endgroup$
add a comment |
$begingroup$
A population $prod$ and a measure $X$ on $prod$ produced the data set below
$71, 80, 58, 60, 63, 64, 51, 55, 48, 67$
Let $h_X$ denote the density histogram function of $X$ based on the four intervals
$(47, 54.2], (54.2, 63.4], (63.4, 67.8]$ and $(67.8, 81]$
$(a)$ Calculate $h_X(75.5)$
$(b)$ Calculate $int_{54.2}^{67.8} h_X(x) dx$
attempt
$(a)$ I made a table
begin{array}{|c|c|c|c|}
hline
interval& (47, 54.2] & (54.2, 63.4] & (63.4, 67.8] & (67.8, 81] \ hline
frequency & 2/10& 4/10& 2/10 & 2/10\ hline
length & 7.2 & 9.2 & 4.4 & 13.2\ hline
h_X(x) & frac{0.2}{7.2} & frac{0.4}{9.2} & frac{0.2}{4.4} & frac{0.2}{13.2} \ hline
end{array}
Therefore $h_X(75.5)$ lies in $(67.8, 81]$
$h_X(75.5) = frac{0.2}{13.2}$
(b)
$int_{54.2}^{67.8} h_X(x) = F_X(67.8) - F_X(54.2) = frac{8}{10} - frac{2}{10} = frac{6}{10}$
is this correct?
statistics
asked Jan 30 at 20:04
Bas basBas bas
49512
$endgroup$
A population $prod$ and a measure $X$ on $prod$ produced the data set below
$71, 80, 58, 60, 63, 64, 51, 55, 48, 67$
Let $h_X$ denote the density histogram function of $X$ based on the four intervals
$(47, 54.2], (54.2, 63.4], (63.4, 67.8]$ and $(67.8, 81]$
$(a)$ Calculate $h_X(75.5)$
$(b)$ Calculate $int_{54.2}^{67.8} h_X(x) dx$
attempt
$(a)$ I made a table
begin{array}{|c|c|c|c|}
hline
interval& (47, 54.2] & (54.2, 63.4] & (63.4, 67.8] & (67.8, 81] \ hline
frequency & 2/10& 4/10& 2/10 & 2/10\ hline
length & 7.2 & 9.2 & 4.4 & 13.2\ hline
h_X(x) & frac{0.2}{7.2} & frac{0.4}{9.2} & frac{0.2}{4.4} & frac{0.2}{13.2} \ hline
end{array}
Therefore $h_X(75.5)$ lies in $(67.8, 81]$
$h_X(75.5) = frac{0.2}{13.2}$
(b)
$int_{54.2}^{67.8} h_X(x) = F_X(67.8) - F_X(54.2) = frac{8}{10} - frac{2}{10} = frac{6}{10}$
is this correct?
statistics
statistics
asked Jan 30 at 20:04
Bas basBas bas
49512
asked Jan 30 at 20:04
Bas basBas bas
49512
asked Jan 30 at 20:04
Bas basBas bas
49512
asked Jan 30 at 20:04
Bas basBas bas
49512
asked Jan 30 at 20:04
Bas basBas bas
49512
49512
add a comment |
add a comment |
0
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',
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%2f3094037%2fcalculating-histogram-function-h-x75-5-and-int-54-267-8-h-xx%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
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%2f3094037%2fcalculating-histogram-function-h-x75-5-and-int-54-267-8-h-xx%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
