Calculating the density function of a variable based on a relation [closed]
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i was wondering how to get density function from a mass function for another density function
probability integration functions density-function
asked Dec 6 '18 at 13:54
Danie BaderDanie Bader
83
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closed as off-topic by José Carlos Santos, Brahadeesh, amWhy, Shailesh, Leucippus Dec 10 '18 at 17:40
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." – José Carlos Santos, Brahadeesh, amWhy, Shailesh, Leucippus
If this question can be reworded to fit the rules in the help center, please edit the question.
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$begingroup$
i was wondering how to get density function from a mass function for another density function
probability integration functions density-function
asked Dec 6 '18 at 13:54
Danie BaderDanie Bader
83
$endgroup$
closed as off-topic by José Carlos Santos, Brahadeesh, amWhy, Shailesh, Leucippus Dec 10 '18 at 17:40
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." – José Carlos Santos, Brahadeesh, amWhy, Shailesh, Leucippus
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
$begingroup$
i was wondering how to get density function from a mass function for another density function
probability integration functions density-function
asked Dec 6 '18 at 13:54
Danie BaderDanie Bader
83
$endgroup$
i was wondering how to get density function from a mass function for another density function
probability integration functions density-function
probability integration functions density-function
asked Dec 6 '18 at 13:54
Danie BaderDanie Bader
83
asked Dec 6 '18 at 13:54
Danie BaderDanie Bader
83
edited Dec 10 '18 at 15:16
Danie Bader
asked Dec 6 '18 at 13:54
Danie BaderDanie Bader
83
asked Dec 6 '18 at 13:54
Danie BaderDanie Bader
83
asked Dec 6 '18 at 13:54
Danie BaderDanie Bader
83
83
closed as off-topic by José Carlos Santos, Brahadeesh, amWhy, Shailesh, Leucippus Dec 10 '18 at 17:40
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." – José Carlos Santos, Brahadeesh, amWhy, Shailesh, Leucippus
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by José Carlos Santos, Brahadeesh, amWhy, Shailesh, Leucippus Dec 10 '18 at 17:40
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." – José Carlos Santos, Brahadeesh, amWhy, Shailesh, Leucippus
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
add a comment |
1 Answer
1
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oldest
votes
$begingroup$
$W=e^{-Y}$ takes values in $left(0,e^{-3}right)$ so that $F_{W}left(wright)=1$
if $Wgeq e^{-3}$ and $F_{W}left(wright)=0$ if $Wleq0$.
Consequently we can go for $f_W(w)=0$ for $wnotinleft(0,e^{-3}right)$.
For $winleft(0,e^{-3}right)$ we find $$F_{W}left(wright)=Pleft(e^{-Y}leq wright)=Pleft(-Yleqln wright)=Pleft(Ygeq-ln wright)=1-F_{Y}left(-ln wright)$$
Taking the derivative we find: $$f_{W}left(wright)=-fleft(-ln wright)frac{dleft(-ln wright)}{dw}=frac{fleft(-ln wright)}{w}=frac{e^{ln w+3}}{w}=e^{3}$$
Final result: $$f_{W}left(wright)=begin{cases}
e^{3} & text{if }winleft(0,e^{-3}right)\
0 & text{otherwise}
end{cases}$$
answered Dec 6 '18 at 14:28
drhabdrhab
99k544130
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add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
$W=e^{-Y}$ takes values in $left(0,e^{-3}right)$ so that $F_{W}left(wright)=1$
if $Wgeq e^{-3}$ and $F_{W}left(wright)=0$ if $Wleq0$.
Consequently we can go for $f_W(w)=0$ for $wnotinleft(0,e^{-3}right)$.
For $winleft(0,e^{-3}right)$ we find $$F_{W}left(wright)=Pleft(e^{-Y}leq wright)=Pleft(-Yleqln wright)=Pleft(Ygeq-ln wright)=1-F_{Y}left(-ln wright)$$
Taking the derivative we find: $$f_{W}left(wright)=-fleft(-ln wright)frac{dleft(-ln wright)}{dw}=frac{fleft(-ln wright)}{w}=frac{e^{ln w+3}}{w}=e^{3}$$
Final result: $$f_{W}left(wright)=begin{cases}
e^{3} & text{if }winleft(0,e^{-3}right)\
0 & text{otherwise}
end{cases}$$
answered Dec 6 '18 at 14:28
drhabdrhab
99k544130
$endgroup$
add a comment |
$begingroup$
$W=e^{-Y}$ takes values in $left(0,e^{-3}right)$ so that $F_{W}left(wright)=1$
if $Wgeq e^{-3}$ and $F_{W}left(wright)=0$ if $Wleq0$.
Consequently we can go for $f_W(w)=0$ for $wnotinleft(0,e^{-3}right)$.
For $winleft(0,e^{-3}right)$ we find $$F_{W}left(wright)=Pleft(e^{-Y}leq wright)=Pleft(-Yleqln wright)=Pleft(Ygeq-ln wright)=1-F_{Y}left(-ln wright)$$
Taking the derivative we find: $$f_{W}left(wright)=-fleft(-ln wright)frac{dleft(-ln wright)}{dw}=frac{fleft(-ln wright)}{w}=frac{e^{ln w+3}}{w}=e^{3}$$
Final result: $$f_{W}left(wright)=begin{cases}
e^{3} & text{if }winleft(0,e^{-3}right)\
0 & text{otherwise}
end{cases}$$
answered Dec 6 '18 at 14:28
drhabdrhab
99k544130
$endgroup$
add a comment |
$begingroup$
$W=e^{-Y}$ takes values in $left(0,e^{-3}right)$ so that $F_{W}left(wright)=1$
if $Wgeq e^{-3}$ and $F_{W}left(wright)=0$ if $Wleq0$.
Consequently we can go for $f_W(w)=0$ for $wnotinleft(0,e^{-3}right)$.
For $winleft(0,e^{-3}right)$ we find $$F_{W}left(wright)=Pleft(e^{-Y}leq wright)=Pleft(-Yleqln wright)=Pleft(Ygeq-ln wright)=1-F_{Y}left(-ln wright)$$
Taking the derivative we find: $$f_{W}left(wright)=-fleft(-ln wright)frac{dleft(-ln wright)}{dw}=frac{fleft(-ln wright)}{w}=frac{e^{ln w+3}}{w}=e^{3}$$
Final result: $$f_{W}left(wright)=begin{cases}
e^{3} & text{if }winleft(0,e^{-3}right)\
0 & text{otherwise}
end{cases}$$
answered Dec 6 '18 at 14:28
drhabdrhab
99k544130
$endgroup$
$W=e^{-Y}$ takes values in $left(0,e^{-3}right)$ so that $F_{W}left(wright)=1$
if $Wgeq e^{-3}$ and $F_{W}left(wright)=0$ if $Wleq0$.
Consequently we can go for $f_W(w)=0$ for $wnotinleft(0,e^{-3}right)$.
For $winleft(0,e^{-3}right)$ we find $$F_{W}left(wright)=Pleft(e^{-Y}leq wright)=Pleft(-Yleqln wright)=Pleft(Ygeq-ln wright)=1-F_{Y}left(-ln wright)$$
Taking the derivative we find: $$f_{W}left(wright)=-fleft(-ln wright)frac{dleft(-ln wright)}{dw}=frac{fleft(-ln wright)}{w}=frac{e^{ln w+3}}{w}=e^{3}$$
Final result: $$f_{W}left(wright)=begin{cases}
e^{3} & text{if }winleft(0,e^{-3}right)\
0 & text{otherwise}
end{cases}$$
answered Dec 6 '18 at 14:28
drhabdrhab
99k544130
answered Dec 6 '18 at 14:28
drhabdrhab
99k544130
answered Dec 6 '18 at 14:28
drhabdrhab
99k544130
answered Dec 6 '18 at 14:28
drhabdrhab
99k544130
99k544130
add a comment |
add a comment |
