Hill climber expected number of steps
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Let's say you're trying to climb a hill with $k$ steps and you have $frac{1}{2}$ chance of climbing one step and $frac{1}{2}$ chance of falling back to the beginning of the hill. I am trying to find the expected number of steps to reach the top of the hill. After reasoning, it's clear that a misstep doubles the number of steps and a correct step increments the total number of steps. I'm not sure how to proceed, given that it's conceivable to get stuck in a potentially infinite loop of stepping up and then falling.
algorithms recursion
asked Jan 16 at 0:52
faeophytafaeophyta
104
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add a comment |
$begingroup$
Let's say you're trying to climb a hill with $k$ steps and you have $frac{1}{2}$ chance of climbing one step and $frac{1}{2}$ chance of falling back to the beginning of the hill. I am trying to find the expected number of steps to reach the top of the hill. After reasoning, it's clear that a misstep doubles the number of steps and a correct step increments the total number of steps. I'm not sure how to proceed, given that it's conceivable to get stuck in a potentially infinite loop of stepping up and then falling.
algorithms recursion
asked Jan 16 at 0:52
faeophytafaeophyta
104
$endgroup$
2
$begingroup$
Equivalent to this problem, generalized: math.stackexchange.com/questions/364038/…
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– T. Fo
Jan 16 at 0:56
add a comment |
$begingroup$
Let's say you're trying to climb a hill with $k$ steps and you have $frac{1}{2}$ chance of climbing one step and $frac{1}{2}$ chance of falling back to the beginning of the hill. I am trying to find the expected number of steps to reach the top of the hill. After reasoning, it's clear that a misstep doubles the number of steps and a correct step increments the total number of steps. I'm not sure how to proceed, given that it's conceivable to get stuck in a potentially infinite loop of stepping up and then falling.
algorithms recursion
asked Jan 16 at 0:52
faeophytafaeophyta
104
$endgroup$
Let's say you're trying to climb a hill with $k$ steps and you have $frac{1}{2}$ chance of climbing one step and $frac{1}{2}$ chance of falling back to the beginning of the hill. I am trying to find the expected number of steps to reach the top of the hill. After reasoning, it's clear that a misstep doubles the number of steps and a correct step increments the total number of steps. I'm not sure how to proceed, given that it's conceivable to get stuck in a potentially infinite loop of stepping up and then falling.
algorithms recursion
algorithms recursion
asked Jan 16 at 0:52
faeophytafaeophyta
104
asked Jan 16 at 0:52
faeophytafaeophyta
104
asked Jan 16 at 0:52
faeophytafaeophyta
104
asked Jan 16 at 0:52
faeophytafaeophyta
104
asked Jan 16 at 0:52
faeophytafaeophyta
104
104
2
$begingroup$
Equivalent to this problem, generalized: math.stackexchange.com/questions/364038/…
$endgroup$
– T. Fo
Jan 16 at 0:56
add a comment |
2
$begingroup$
Equivalent to this problem, generalized: math.stackexchange.com/questions/364038/…
$endgroup$
– T. Fo
Jan 16 at 0:56
2
2
$begingroup$
Equivalent to this problem, generalized: math.stackexchange.com/questions/364038/…
$endgroup$
– T. Fo
Jan 16 at 0:56
$begingroup$
Equivalent to this problem, generalized: math.stackexchange.com/questions/364038/…
$endgroup$
– T. Fo
Jan 16 at 0:56
add a comment |
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$begingroup$
Equivalent to this problem, generalized: math.stackexchange.com/questions/364038/…
$endgroup$
– T. Fo
Jan 16 at 0:56