Upper bound probability of variable that decreases at every step
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I'm having a hard time wrapping my mind around this small probability problem.
We start with a variable $X$, that has some fixed integer value in $[d,n]$. At each step, there is a $frac{X}{n}$ chance that we decrease the value of $X$ by 1. We repeat this $m$ times.
What is an upper bound on the probability that the value of $X$ is $geq d$ at the end of this?
probability
asked Nov 15 at 3:07
Claire Chen
133
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up vote
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I'm having a hard time wrapping my mind around this small probability problem.
We start with a variable $X$, that has some fixed integer value in $[d,n]$. At each step, there is a $frac{X}{n}$ chance that we decrease the value of $X$ by 1. We repeat this $m$ times.
What is an upper bound on the probability that the value of $X$ is $geq d$ at the end of this?
probability
asked Nov 15 at 3:07
Claire Chen
133
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I'm having a hard time wrapping my mind around this small probability problem.
We start with a variable $X$, that has some fixed integer value in $[d,n]$. At each step, there is a $frac{X}{n}$ chance that we decrease the value of $X$ by 1. We repeat this $m$ times.
What is an upper bound on the probability that the value of $X$ is $geq d$ at the end of this?
probability
asked Nov 15 at 3:07
Claire Chen
133
I'm having a hard time wrapping my mind around this small probability problem.
We start with a variable $X$, that has some fixed integer value in $[d,n]$. At each step, there is a $frac{X}{n}$ chance that we decrease the value of $X$ by 1. We repeat this $m$ times.
What is an upper bound on the probability that the value of $X$ is $geq d$ at the end of this?
probability
probability
asked Nov 15 at 3:07
Claire Chen
133
asked Nov 15 at 3:07
Claire Chen
133
asked Nov 15 at 3:07
Claire Chen
133
asked Nov 15 at 3:07
Claire Chen
133
asked Nov 15 at 3:07
Claire Chen
133
133
add a comment |
add a comment |
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