Upper bounds for two events of random variable following Poisson distributionConditional probability involving Poisson random variableWhat is the time between groups of events when single events have a Poisson distribution?Inter-event time between 1st and 2nd events for Poisson ProcessBounds on Poisson Random VariableUpper/lower bound on variance of positive random variableUsing chernoff bounds for poisson distributionCombined Poisson Random VariableExpected Value of Poisson Distribution depending on Random Variable with Exponential DistributionRequest arrival following Poisson distributionThe probability distribution for the waiting time between two clients.
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Upper bounds for two events of random variable following Poisson distribution
Conditional probability involving Poisson random variableWhat is the time between groups of events when single events have a Poisson distribution?Inter-event time between 1st and 2nd events for Poisson ProcessBounds on Poisson Random VariableUpper/lower bound on variance of positive random variableUsing chernoff bounds for poisson distributionCombined Poisson Random VariableExpected Value of Poisson Distribution depending on Random Variable with Exponential DistributionRequest arrival following Poisson distributionThe probability distribution for the waiting time between two clients.
$begingroup$
So $X$ follows Poisson with $L>0$ and $operatornameE[X]=operatornameVar(X)=L$. We are dealing with two events:
$A=X leq L/2$ and $B=X geq 2L$. I have calculated that $P(A) leq 4/L$ and $P(B) leq 1/L$ and I want to calculate the upper bound for $P(A cup B)$. Any ideas?
inequality poisson-distribution
edited Mar 13 at 9:40
Rócherz
2,9863821
asked Mar 13 at 9:34
EmKalEmKal
11
New contributor
EmKal is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
So $X$ follows Poisson with $L>0$ and $operatornameE[X]=operatornameVar(X)=L$. We are dealing with two events:
$A=X leq L/2$ and $B=X geq 2L$. I have calculated that $P(A) leq 4/L$ and $P(B) leq 1/L$ and I want to calculate the upper bound for $P(A cup B)$. Any ideas?
inequality poisson-distribution
edited Mar 13 at 9:40
Rócherz
2,9863821
asked Mar 13 at 9:34
EmKalEmKal
11
New contributor
EmKal is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
1
$begingroup$
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
$endgroup$
– José Carlos Santos
Mar 13 at 9:35
add a comment |
$begingroup$
So $X$ follows Poisson with $L>0$ and $operatornameE[X]=operatornameVar(X)=L$. We are dealing with two events:
$A=X leq L/2$ and $B=X geq 2L$. I have calculated that $P(A) leq 4/L$ and $P(B) leq 1/L$ and I want to calculate the upper bound for $P(A cup B)$. Any ideas?
inequality poisson-distribution
edited Mar 13 at 9:40
Rócherz
2,9863821
asked Mar 13 at 9:34
EmKalEmKal
11
New contributor
EmKal is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
So $X$ follows Poisson with $L>0$ and $operatornameE[X]=operatornameVar(X)=L$. We are dealing with two events:
$A=X leq L/2$ and $B=X geq 2L$. I have calculated that $P(A) leq 4/L$ and $P(B) leq 1/L$ and I want to calculate the upper bound for $P(A cup B)$. Any ideas?
inequality poisson-distribution
inequality poisson-distribution
edited Mar 13 at 9:40
Rócherz
2,9863821
asked Mar 13 at 9:34
EmKalEmKal
11
New contributor
EmKal is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited Mar 13 at 9:40
Rócherz
2,9863821
asked Mar 13 at 9:34
EmKalEmKal
11
New contributor
EmKal is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited Mar 13 at 9:40
Rócherz
2,9863821
edited Mar 13 at 9:40
Rócherz
2,9863821
edited Mar 13 at 9:40
Rócherz
2,9863821
2,9863821
asked Mar 13 at 9:34
EmKalEmKal
11
New contributor
EmKal is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Mar 13 at 9:34
EmKalEmKal
11
asked Mar 13 at 9:34
EmKalEmKal
11
11
New contributor
EmKal is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
EmKal is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
EmKal is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
1
$begingroup$
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
$endgroup$
– José Carlos Santos
Mar 13 at 9:35
add a comment |
1
$begingroup$
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
$endgroup$
– José Carlos Santos
Mar 13 at 9:35
1
1
$begingroup$
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
$endgroup$
– José Carlos Santos
Mar 13 at 9:35
$begingroup$
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
$endgroup$
– José Carlos Santos
Mar 13 at 9:35
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
$$Acap B=left2Lle xle Lover 2right=emptyset\to\Pr(Acup B)=Pr(A)+Pr(B)-Pr(Acap B)\=Pr(A)+Pr(B)\le 5over L$$therefore $$Pr(Acup B)le 5over L$$
answered Mar 13 at 12:11
Mostafa AyazMostafa Ayaz
16.5k3939
$endgroup$
$begingroup$
That was indeed my answer which is the sum of P(A),P(B) : 1/L+4/L=5/L. However my teacher asks (since we are using Chebyshev's inequality) a better value i.e least upper bound if I understood correctly. Your thoughts please.
$endgroup$
– EmKal
Mar 13 at 13:14
$begingroup$
Unfortunately I couldn't find any better upper bound using Chebyshev's inequality. Of course the exact value can be found which I don't think to be the main purpose here :)
$endgroup$
– Mostafa Ayaz
Mar 13 at 21:30
$begingroup$
Please share it with me. I appreciate your assistance.
$endgroup$
– EmKal
Mar 14 at 12:33
add a comment |
Your Answer
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1 Answer
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1 Answer
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$begingroup$
$$Acap B=left2Lle xle Lover 2right=emptyset\to\Pr(Acup B)=Pr(A)+Pr(B)-Pr(Acap B)\=Pr(A)+Pr(B)\le 5over L$$therefore $$Pr(Acup B)le 5over L$$
answered Mar 13 at 12:11
Mostafa AyazMostafa Ayaz
16.5k3939
$endgroup$
$begingroup$
That was indeed my answer which is the sum of P(A),P(B) : 1/L+4/L=5/L. However my teacher asks (since we are using Chebyshev's inequality) a better value i.e least upper bound if I understood correctly. Your thoughts please.
$endgroup$
– EmKal
Mar 13 at 13:14
$begingroup$
Unfortunately I couldn't find any better upper bound using Chebyshev's inequality. Of course the exact value can be found which I don't think to be the main purpose here :)
$endgroup$
– Mostafa Ayaz
Mar 13 at 21:30
$begingroup$
Please share it with me. I appreciate your assistance.
$endgroup$
– EmKal
Mar 14 at 12:33
add a comment |
$begingroup$
$$Acap B=left2Lle xle Lover 2right=emptyset\to\Pr(Acup B)=Pr(A)+Pr(B)-Pr(Acap B)\=Pr(A)+Pr(B)\le 5over L$$therefore $$Pr(Acup B)le 5over L$$
answered Mar 13 at 12:11
Mostafa AyazMostafa Ayaz
16.5k3939
$endgroup$
$begingroup$
That was indeed my answer which is the sum of P(A),P(B) : 1/L+4/L=5/L. However my teacher asks (since we are using Chebyshev's inequality) a better value i.e least upper bound if I understood correctly. Your thoughts please.
$endgroup$
– EmKal
Mar 13 at 13:14
$begingroup$
Unfortunately I couldn't find any better upper bound using Chebyshev's inequality. Of course the exact value can be found which I don't think to be the main purpose here :)
$endgroup$
– Mostafa Ayaz
Mar 13 at 21:30
$begingroup$
Please share it with me. I appreciate your assistance.
$endgroup$
– EmKal
Mar 14 at 12:33
add a comment |
$begingroup$
$$Acap B=left2Lle xle Lover 2right=emptyset\to\Pr(Acup B)=Pr(A)+Pr(B)-Pr(Acap B)\=Pr(A)+Pr(B)\le 5over L$$therefore $$Pr(Acup B)le 5over L$$
answered Mar 13 at 12:11
Mostafa AyazMostafa Ayaz
16.5k3939
$endgroup$
$$Acap B=left2Lle xle Lover 2right=emptyset\to\Pr(Acup B)=Pr(A)+Pr(B)-Pr(Acap B)\=Pr(A)+Pr(B)\le 5over L$$therefore $$Pr(Acup B)le 5over L$$
answered Mar 13 at 12:11
Mostafa AyazMostafa Ayaz
16.5k3939
answered Mar 13 at 12:11
Mostafa AyazMostafa Ayaz
16.5k3939
answered Mar 13 at 12:11
Mostafa AyazMostafa Ayaz
16.5k3939
answered Mar 13 at 12:11
Mostafa AyazMostafa Ayaz
16.5k3939
16.5k3939
$begingroup$
That was indeed my answer which is the sum of P(A),P(B) : 1/L+4/L=5/L. However my teacher asks (since we are using Chebyshev's inequality) a better value i.e least upper bound if I understood correctly. Your thoughts please.
$endgroup$
– EmKal
Mar 13 at 13:14
$begingroup$
Unfortunately I couldn't find any better upper bound using Chebyshev's inequality. Of course the exact value can be found which I don't think to be the main purpose here :)
$endgroup$
– Mostafa Ayaz
Mar 13 at 21:30
$begingroup$
Please share it with me. I appreciate your assistance.
$endgroup$
– EmKal
Mar 14 at 12:33
add a comment |
$begingroup$
That was indeed my answer which is the sum of P(A),P(B) : 1/L+4/L=5/L. However my teacher asks (since we are using Chebyshev's inequality) a better value i.e least upper bound if I understood correctly. Your thoughts please.
$endgroup$
– EmKal
Mar 13 at 13:14
$begingroup$
Unfortunately I couldn't find any better upper bound using Chebyshev's inequality. Of course the exact value can be found which I don't think to be the main purpose here :)
$endgroup$
– Mostafa Ayaz
Mar 13 at 21:30
$begingroup$
Please share it with me. I appreciate your assistance.
$endgroup$
– EmKal
Mar 14 at 12:33
$begingroup$
That was indeed my answer which is the sum of P(A),P(B) : 1/L+4/L=5/L. However my teacher asks (since we are using Chebyshev's inequality) a better value i.e least upper bound if I understood correctly. Your thoughts please.
$endgroup$
– EmKal
Mar 13 at 13:14
$begingroup$
That was indeed my answer which is the sum of P(A),P(B) : 1/L+4/L=5/L. However my teacher asks (since we are using Chebyshev's inequality) a better value i.e least upper bound if I understood correctly. Your thoughts please.
$endgroup$
– EmKal
Mar 13 at 13:14
$begingroup$
Unfortunately I couldn't find any better upper bound using Chebyshev's inequality. Of course the exact value can be found which I don't think to be the main purpose here :)
$endgroup$
– Mostafa Ayaz
Mar 13 at 21:30
$begingroup$
Unfortunately I couldn't find any better upper bound using Chebyshev's inequality. Of course the exact value can be found which I don't think to be the main purpose here :)
$endgroup$
– Mostafa Ayaz
Mar 13 at 21:30
$begingroup$
Please share it with me. I appreciate your assistance.
$endgroup$
– EmKal
Mar 14 at 12:33
$begingroup$
Please share it with me. I appreciate your assistance.
$endgroup$
– EmKal
Mar 14 at 12:33
add a comment |
EmKal is a new contributor. Be nice, and check out our Code of Conduct.
EmKal is a new contributor. Be nice, and check out our Code of Conduct.
EmKal is a new contributor. Be nice, and check out our Code of Conduct.
EmKal is a new contributor. Be nice, and check out our Code of Conduct.
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$begingroup$
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
$endgroup$
– José Carlos Santos
Mar 13 at 9:35