Probability of min(x,y)<1 [on hold]
How can I solve this?
$f_{xy}(x,y)$ is a joint probability distribution defined by
$$f_{xy}(x,y)=ye^{-y(1+x)}$$ for $ x,y>0$.
And for other $x,y$ the joint probability distribution defiend by
$$f_{xy}(x,y)=0$$
And the Question is Find the probability of:
P(min(x,y)<1)=?
Please Write Your Full Answer.
probability
asked yesterday
Mobina K
134
New contributor
Mobina K is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
put on hold as off-topic by Eevee Trainer, StubbornAtom, Lee David Chung Lin, Saad, caverac 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." – Eevee Trainer, Lee David Chung Lin, Saad
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
How can I solve this?
$f_{xy}(x,y)$ is a joint probability distribution defined by
$$f_{xy}(x,y)=ye^{-y(1+x)}$$ for $ x,y>0$.
And for other $x,y$ the joint probability distribution defiend by
$$f_{xy}(x,y)=0$$
And the Question is Find the probability of:
P(min(x,y)<1)=?
Please Write Your Full Answer.
probability
asked yesterday
Mobina K
134
New contributor
Mobina K is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
put on hold as off-topic by Eevee Trainer, StubbornAtom, Lee David Chung Lin, Saad, caverac 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." – Eevee Trainer, Lee David Chung Lin, Saad
If this question can be reworded to fit the rules in the help center, please edit the question.
1
Draw the region ${min(x,y) < 1}$ on the $x$-$y$ plane and integrate the density over that region.
– angryavian
yesterday
1
Possible duplicate of Can You Help me ?A simple Probability Question
– StubbornAtom
yesterday
add a comment |
How can I solve this?
$f_{xy}(x,y)$ is a joint probability distribution defined by
$$f_{xy}(x,y)=ye^{-y(1+x)}$$ for $ x,y>0$.
And for other $x,y$ the joint probability distribution defiend by
$$f_{xy}(x,y)=0$$
And the Question is Find the probability of:
P(min(x,y)<1)=?
Please Write Your Full Answer.
probability
asked yesterday
Mobina K
134
New contributor
Mobina K is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
How can I solve this?
$f_{xy}(x,y)$ is a joint probability distribution defined by
$$f_{xy}(x,y)=ye^{-y(1+x)}$$ for $ x,y>0$.
And for other $x,y$ the joint probability distribution defiend by
$$f_{xy}(x,y)=0$$
And the Question is Find the probability of:
P(min(x,y)<1)=?
Please Write Your Full Answer.
probability
probability
asked yesterday
Mobina K
134
New contributor
Mobina K is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked yesterday
Mobina K
134
New contributor
Mobina K is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked yesterday
Mobina K
134
New contributor
Mobina K is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked yesterday
Mobina K
134
asked yesterday
Mobina K
134
134
New contributor
Mobina K is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Mobina K is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Mobina K is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
put on hold as off-topic by Eevee Trainer, StubbornAtom, Lee David Chung Lin, Saad, caverac 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." – Eevee Trainer, Lee David Chung Lin, Saad
If this question can be reworded to fit the rules in the help center, please edit the question.
put on hold as off-topic by Eevee Trainer, StubbornAtom, Lee David Chung Lin, Saad, caverac 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." – Eevee Trainer, Lee David Chung Lin, Saad
If this question can be reworded to fit the rules in the help center, please edit the question.
1
Draw the region ${min(x,y) < 1}$ on the $x$-$y$ plane and integrate the density over that region.
– angryavian
yesterday
1
Possible duplicate of Can You Help me ?A simple Probability Question
– StubbornAtom
yesterday
add a comment |
1
Draw the region ${min(x,y) < 1}$ on the $x$-$y$ plane and integrate the density over that region.
– angryavian
yesterday
1
Possible duplicate of Can You Help me ?A simple Probability Question
– StubbornAtom
yesterday
1
1
Draw the region ${min(x,y) < 1}$ on the $x$-$y$ plane and integrate the density over that region.
– angryavian
yesterday
Draw the region ${min(x,y) < 1}$ on the $x$-$y$ plane and integrate the density over that region.
– angryavian
yesterday
1
1
Possible duplicate of Can You Help me ?A simple Probability Question
– StubbornAtom
yesterday
Possible duplicate of Can You Help me ?A simple Probability Question
– StubbornAtom
yesterday
add a comment |
1 Answer
1
active
oldest
votes
$$P(min(x,y)<1)=1-P(min(x,y)geq 1) = 1-P(xgeq 1,ygeq 1)$$
$$ = 1-int_{1}^{infty} int_{1}^{infty} ye^{-y(x+1)}dxdy.$$
So we have that
$$P(min(x,y)<1) = 1-int_{1}^{infty}e^{-(y+1)}dy=1-frac{1}{e^2}.$$
answered yesterday
Hello_World
4,11621630
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$$P(min(x,y)<1)=1-P(min(x,y)geq 1) = 1-P(xgeq 1,ygeq 1)$$
$$ = 1-int_{1}^{infty} int_{1}^{infty} ye^{-y(x+1)}dxdy.$$
So we have that
$$P(min(x,y)<1) = 1-int_{1}^{infty}e^{-(y+1)}dy=1-frac{1}{e^2}.$$
answered yesterday
Hello_World
4,11621630
add a comment |
$$P(min(x,y)<1)=1-P(min(x,y)geq 1) = 1-P(xgeq 1,ygeq 1)$$
$$ = 1-int_{1}^{infty} int_{1}^{infty} ye^{-y(x+1)}dxdy.$$
So we have that
$$P(min(x,y)<1) = 1-int_{1}^{infty}e^{-(y+1)}dy=1-frac{1}{e^2}.$$
answered yesterday
Hello_World
4,11621630
add a comment |
$$P(min(x,y)<1)=1-P(min(x,y)geq 1) = 1-P(xgeq 1,ygeq 1)$$
$$ = 1-int_{1}^{infty} int_{1}^{infty} ye^{-y(x+1)}dxdy.$$
So we have that
$$P(min(x,y)<1) = 1-int_{1}^{infty}e^{-(y+1)}dy=1-frac{1}{e^2}.$$
answered yesterday
Hello_World
4,11621630
$$P(min(x,y)<1)=1-P(min(x,y)geq 1) = 1-P(xgeq 1,ygeq 1)$$
$$ = 1-int_{1}^{infty} int_{1}^{infty} ye^{-y(x+1)}dxdy.$$
So we have that
$$P(min(x,y)<1) = 1-int_{1}^{infty}e^{-(y+1)}dy=1-frac{1}{e^2}.$$
answered yesterday
Hello_World
4,11621630
answered yesterday
Hello_World
4,11621630
answered yesterday
Hello_World
4,11621630
answered yesterday
Hello_World
4,11621630
4,11621630
add a comment |
add a comment |
1
Draw the region ${min(x,y) < 1}$ on the $x$-$y$ plane and integrate the density over that region.
– angryavian
yesterday
1
Possible duplicate of Can You Help me ?A simple Probability Question
– StubbornAtom
yesterday