How do I find the marginal density functions [on hold] The Next CEO of Stack OverflowHow to find the probability of variables with joint density?probability, need help on the marginal densitiesMarginal DensitiesIntegral for marginal density of transformed rv doesn't convergeFinding domain of variables in joint density for marginal densityJoint and Marginal DensitiesFinding the marginal density when the conditional density is given to us.Find the marginal distribution of an point randomly chosen on an ellipseCalculation marginal density functions given a multi-variable PDFHow do I determine independence without computing $f_X (x)$ and $f_Y(y)$?
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How do I find the marginal density functions [on hold]
The Next CEO of Stack OverflowHow to find the probability of variables with joint density?probability, need help on the marginal densitiesMarginal DensitiesIntegral for marginal density of transformed rv doesn't convergeFinding domain of variables in joint density for marginal densityJoint and Marginal DensitiesFinding the marginal density when the conditional density is given to us.Find the marginal distribution of an point randomly chosen on an ellipseCalculation marginal density functions given a multi-variable PDFHow do I determine independence without computing $f_X (x)$ and $f_Y(y)$?
$begingroup$
Let 𝑋 be the percentage of completion of a certain task in an airtight factory machine, and let 𝑌 be the pressure in the closed space in atmospheres (where 1 atmosphere is 101.325 kPa). Take 𝑋 and 𝑌 as two random variables with the following joint probability density function. Assume 𝑘 is a constant multiplier which satisfies that the density integrates to 1. For this question you do not have to determine what 𝑘 is.
𝑓(𝑥,𝑦)=⎧⎩⎨⎪⎪𝑘[(𝑥𝑦)2𝑒^(x+y) ln(𝑦^x)+y^2⋅𝑒^y⋅ln(𝑦)], 0.5≤𝑥≤1≤𝑦≤1.50, otherwise
(a) Are the percentage of completion of the task and the pressure in the chamber independent? Show your reasoning.
(b) What is the correlation between the percentage completion of the task and the pressure in the chamber? If you need to use k you do not need to solve for k.
(c) Feel free to define a as a constant multiplier so that the marginal density 𝑓𝑋(𝑥) integrates to 1, and define b as a constant multiplier so that the marginal density 𝑓𝑌(𝑦) integrates to 1. Without having to solve for a or b, write these two marginal density functions. How do a and b relate to k?
I'm stuck on part c with finding the marginal densities
probability statistics
asked Mar 27 at 18:41
RitaRita
24
$endgroup$
put on hold as off-topic by StubbornAtom, YiFan, Adrian Keister, Strants, Cesareo yesterday
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – StubbornAtom, YiFan, Adrian Keister, Cesareo
add a comment |
$begingroup$
Let 𝑋 be the percentage of completion of a certain task in an airtight factory machine, and let 𝑌 be the pressure in the closed space in atmospheres (where 1 atmosphere is 101.325 kPa). Take 𝑋 and 𝑌 as two random variables with the following joint probability density function. Assume 𝑘 is a constant multiplier which satisfies that the density integrates to 1. For this question you do not have to determine what 𝑘 is.
𝑓(𝑥,𝑦)=⎧⎩⎨⎪⎪𝑘[(𝑥𝑦)2𝑒^(x+y) ln(𝑦^x)+y^2⋅𝑒^y⋅ln(𝑦)], 0.5≤𝑥≤1≤𝑦≤1.50, otherwise
(a) Are the percentage of completion of the task and the pressure in the chamber independent? Show your reasoning.
(b) What is the correlation between the percentage completion of the task and the pressure in the chamber? If you need to use k you do not need to solve for k.
(c) Feel free to define a as a constant multiplier so that the marginal density 𝑓𝑋(𝑥) integrates to 1, and define b as a constant multiplier so that the marginal density 𝑓𝑌(𝑦) integrates to 1. Without having to solve for a or b, write these two marginal density functions. How do a and b relate to k?
I'm stuck on part c with finding the marginal densities
probability statistics
asked Mar 27 at 18:41
RitaRita
24
$endgroup$
put on hold as off-topic by StubbornAtom, YiFan, Adrian Keister, Strants, Cesareo yesterday
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – StubbornAtom, YiFan, Adrian Keister, Cesareo
6
$begingroup$
Please use MathJax to format your question.
$endgroup$
– saulspatz
Mar 27 at 18:42
add a comment |
$begingroup$
Let 𝑋 be the percentage of completion of a certain task in an airtight factory machine, and let 𝑌 be the pressure in the closed space in atmospheres (where 1 atmosphere is 101.325 kPa). Take 𝑋 and 𝑌 as two random variables with the following joint probability density function. Assume 𝑘 is a constant multiplier which satisfies that the density integrates to 1. For this question you do not have to determine what 𝑘 is.
𝑓(𝑥,𝑦)=⎧⎩⎨⎪⎪𝑘[(𝑥𝑦)2𝑒^(x+y) ln(𝑦^x)+y^2⋅𝑒^y⋅ln(𝑦)], 0.5≤𝑥≤1≤𝑦≤1.50, otherwise
(a) Are the percentage of completion of the task and the pressure in the chamber independent? Show your reasoning.
(b) What is the correlation between the percentage completion of the task and the pressure in the chamber? If you need to use k you do not need to solve for k.
(c) Feel free to define a as a constant multiplier so that the marginal density 𝑓𝑋(𝑥) integrates to 1, and define b as a constant multiplier so that the marginal density 𝑓𝑌(𝑦) integrates to 1. Without having to solve for a or b, write these two marginal density functions. How do a and b relate to k?
I'm stuck on part c with finding the marginal densities
probability statistics
asked Mar 27 at 18:41
RitaRita
24
$endgroup$
Let 𝑋 be the percentage of completion of a certain task in an airtight factory machine, and let 𝑌 be the pressure in the closed space in atmospheres (where 1 atmosphere is 101.325 kPa). Take 𝑋 and 𝑌 as two random variables with the following joint probability density function. Assume 𝑘 is a constant multiplier which satisfies that the density integrates to 1. For this question you do not have to determine what 𝑘 is.
𝑓(𝑥,𝑦)=⎧⎩⎨⎪⎪𝑘[(𝑥𝑦)2𝑒^(x+y) ln(𝑦^x)+y^2⋅𝑒^y⋅ln(𝑦)], 0.5≤𝑥≤1≤𝑦≤1.50, otherwise
(a) Are the percentage of completion of the task and the pressure in the chamber independent? Show your reasoning.
(b) What is the correlation between the percentage completion of the task and the pressure in the chamber? If you need to use k you do not need to solve for k.
(c) Feel free to define a as a constant multiplier so that the marginal density 𝑓𝑋(𝑥) integrates to 1, and define b as a constant multiplier so that the marginal density 𝑓𝑌(𝑦) integrates to 1. Without having to solve for a or b, write these two marginal density functions. How do a and b relate to k?
I'm stuck on part c with finding the marginal densities
probability statistics
probability statistics
asked Mar 27 at 18:41
RitaRita
24
asked Mar 27 at 18:41
RitaRita
24
edited Mar 27 at 19:10
Rita
asked Mar 27 at 18:41
RitaRita
24
asked Mar 27 at 18:41
RitaRita
24
asked Mar 27 at 18:41
RitaRita
24
24
put on hold as off-topic by StubbornAtom, YiFan, Adrian Keister, Strants, Cesareo yesterday
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – StubbornAtom, YiFan, Adrian Keister, Cesareo
put on hold as off-topic by StubbornAtom, YiFan, Adrian Keister, Strants, Cesareo yesterday
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – StubbornAtom, YiFan, Adrian Keister, Cesareo
6
$begingroup$
Please use MathJax to format your question.
$endgroup$
– saulspatz
Mar 27 at 18:42
add a comment |
6
$begingroup$
Please use MathJax to format your question.
$endgroup$
– saulspatz
Mar 27 at 18:42
6
6
$begingroup$
Please use MathJax to format your question.
$endgroup$
– saulspatz
Mar 27 at 18:42
$begingroup$
Please use MathJax to format your question.
$endgroup$
– saulspatz
Mar 27 at 18:42
add a comment |
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$begingroup$
Please use MathJax to format your question.
$endgroup$
– saulspatz
Mar 27 at 18:42