Markov inequality for random variables with negative values.
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I'm given the maximum value of a random variable $X$ (for example $50$) and its mean, $mathbb E(X)=20$. How do I find the upper bound to $P(Xle -10)$?
random-variables
edited yesterday
Jimmy R.
32.7k42156
asked yesterday
puffles
1078
add a comment |
up vote
2
down vote
favorite
I'm given the maximum value of a random variable $X$ (for example $50$) and its mean, $mathbb E(X)=20$. How do I find the upper bound to $P(Xle -10)$?
random-variables
edited yesterday
Jimmy R.
32.7k42156
asked yesterday
puffles
1078
1
I think that you need to make the transformation $Y = X + 11$ and work from there.
– Ekesh
yesterday
add a comment |
up vote
2
down vote
favorite
up vote
2
down vote
favorite
I'm given the maximum value of a random variable $X$ (for example $50$) and its mean, $mathbb E(X)=20$. How do I find the upper bound to $P(Xle -10)$?
random-variables
edited yesterday
Jimmy R.
32.7k42156
asked yesterday
puffles
1078
I'm given the maximum value of a random variable $X$ (for example $50$) and its mean, $mathbb E(X)=20$. How do I find the upper bound to $P(Xle -10)$?
random-variables
random-variables
edited yesterday
Jimmy R.
32.7k42156
asked yesterday
puffles
1078
edited yesterday
Jimmy R.
32.7k42156
asked yesterday
puffles
1078
edited yesterday
Jimmy R.
32.7k42156
edited yesterday
Jimmy R.
32.7k42156
edited yesterday
Jimmy R.
32.7k42156
32.7k42156
asked yesterday
puffles
1078
asked yesterday
puffles
1078
asked yesterday
puffles
1078
1078
1
I think that you need to make the transformation $Y = X + 11$ and work from there.
– Ekesh
yesterday
add a comment |
1
I think that you need to make the transformation $Y = X + 11$ and work from there.
– Ekesh
yesterday
1
1
I think that you need to make the transformation $Y = X + 11$ and work from there.
– Ekesh
yesterday
I think that you need to make the transformation $Y = X + 11$ and work from there.
– Ekesh
yesterday
add a comment |
1 Answer
1
active
oldest
votes
up vote
1
down vote
accepted
Hint:
$50-X$ is a nonnegative random variable since $50$ is an upperbound.
Express your inequality in the form of $Pr(50-X ge c)$.
answered yesterday
Siong Thye Goh
92.3k1461114
So it should be like this : P(50-X >= -10) ?
– puffles
yesterday
$P(X le -10) = P(-X ge 10) = P(50-X ge 60)$, now apply Markov on $50-X$.
– Siong Thye Goh
yesterday
Makes sense. Thanks a bunch!
– puffles
yesterday
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
accepted
Hint:
$50-X$ is a nonnegative random variable since $50$ is an upperbound.
Express your inequality in the form of $Pr(50-X ge c)$.
answered yesterday
Siong Thye Goh
92.3k1461114
So it should be like this : P(50-X >= -10) ?
– puffles
yesterday
$P(X le -10) = P(-X ge 10) = P(50-X ge 60)$, now apply Markov on $50-X$.
– Siong Thye Goh
yesterday
Makes sense. Thanks a bunch!
– puffles
yesterday
add a comment |
up vote
1
down vote
accepted
Hint:
$50-X$ is a nonnegative random variable since $50$ is an upperbound.
Express your inequality in the form of $Pr(50-X ge c)$.
answered yesterday
Siong Thye Goh
92.3k1461114
So it should be like this : P(50-X >= -10) ?
– puffles
yesterday
$P(X le -10) = P(-X ge 10) = P(50-X ge 60)$, now apply Markov on $50-X$.
– Siong Thye Goh
yesterday
Makes sense. Thanks a bunch!
– puffles
yesterday
add a comment |
up vote
1
down vote
accepted
up vote
1
down vote
accepted
Hint:
$50-X$ is a nonnegative random variable since $50$ is an upperbound.
Express your inequality in the form of $Pr(50-X ge c)$.
answered yesterday
Siong Thye Goh
92.3k1461114
Hint:
$50-X$ is a nonnegative random variable since $50$ is an upperbound.
Express your inequality in the form of $Pr(50-X ge c)$.
answered yesterday
Siong Thye Goh
92.3k1461114
answered yesterday
Siong Thye Goh
92.3k1461114
answered yesterday
Siong Thye Goh
92.3k1461114
answered yesterday
Siong Thye Goh
92.3k1461114
92.3k1461114
So it should be like this : P(50-X >= -10) ?
– puffles
yesterday
$P(X le -10) = P(-X ge 10) = P(50-X ge 60)$, now apply Markov on $50-X$.
– Siong Thye Goh
yesterday
Makes sense. Thanks a bunch!
– puffles
yesterday
add a comment |
So it should be like this : P(50-X >= -10) ?
– puffles
yesterday
$P(X le -10) = P(-X ge 10) = P(50-X ge 60)$, now apply Markov on $50-X$.
– Siong Thye Goh
yesterday
Makes sense. Thanks a bunch!
– puffles
yesterday
So it should be like this : P(50-X >= -10) ?
– puffles
yesterday
So it should be like this : P(50-X >= -10) ?
– puffles
yesterday
$P(X le -10) = P(-X ge 10) = P(50-X ge 60)$, now apply Markov on $50-X$.
– Siong Thye Goh
yesterday
$P(X le -10) = P(-X ge 10) = P(50-X ge 60)$, now apply Markov on $50-X$.
– Siong Thye Goh
yesterday
Makes sense. Thanks a bunch!
– puffles
yesterday
Makes sense. Thanks a bunch!
– puffles
yesterday
add a comment |
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1
I think that you need to make the transformation $Y = X + 11$ and work from there.
– Ekesh
yesterday