calculating probability of drunk man walking on a line
$begingroup$
I would appreciate if you could check if I obtained the right results:
The problem:
A drunk man is walking in random steps along an axis with the points +-1, +-2,+-3,... each steps he does is in the length of 1 unit with the probability of 0.4 forward and 0.6 backwards(the steps are undependable). X will mark his placement on the axis after 50 steps.
1. What is $p{x=-10}$
My answer:
The probability that the drunken man will be at position $x=-10$ after 50 steps is $0.053$
2. What is the variance of $x$?
My answer:
Using the binomial variance distribution $varleft(xright)=binom{n}{k}p^kleft(1-pright)^{n-k}$ i obtained that the variance is 24
3. What are the odds that his last step ($50$th) will be at $x = -27$?
My answer:
The odds of his last step, the $50$th, will be at position $x = -27$ is $0.130$
4. Assuming the the chances of the drunken man of falling in each step is $0.01$: if the drunken man walks for $2000$ steps, what are the odds in estimation that he will fall exactly $23$ times?
My answer:
I am quite sure I got this one wrong, but after 2000 steps, the probability he'll fall exactly 23 times is $0.72$
Can anyone check if I got the correct results?
EDIT: for some reason when i try to write the full calculations it goes wrong, so i'll explain what i did and which formula i used.
for 1:$C_50,20$ with the given probabilities times $20$ and $30$ accordingly
for 2: using the variance distribution formula along with the given details: $varleft(xright)=binom{n}{k}p^kleft(1-pright)^{n-k}$
for 3: for some reason now i can't find a way to land on $-27$ on the last step(the 50th)
for 4:using the same formula, $c_2000,23$ with 0.1 times 23 and 0.99 times 1977 (calculated using complements(1-p))
probability discrete-mathematics stochastic-processes random-walk
edited Dec 22 '18 at 17:46
Jneven
953322
asked May 1 '18 at 21:15
BeginningMathBeginningMath
59929
$endgroup$
add a comment |
$begingroup$
I would appreciate if you could check if I obtained the right results:
The problem:
A drunk man is walking in random steps along an axis with the points +-1, +-2,+-3,... each steps he does is in the length of 1 unit with the probability of 0.4 forward and 0.6 backwards(the steps are undependable). X will mark his placement on the axis after 50 steps.
1. What is $p{x=-10}$
My answer:
The probability that the drunken man will be at position $x=-10$ after 50 steps is $0.053$
2. What is the variance of $x$?
My answer:
Using the binomial variance distribution $varleft(xright)=binom{n}{k}p^kleft(1-pright)^{n-k}$ i obtained that the variance is 24
3. What are the odds that his last step ($50$th) will be at $x = -27$?
My answer:
The odds of his last step, the $50$th, will be at position $x = -27$ is $0.130$
4. Assuming the the chances of the drunken man of falling in each step is $0.01$: if the drunken man walks for $2000$ steps, what are the odds in estimation that he will fall exactly $23$ times?
My answer:
I am quite sure I got this one wrong, but after 2000 steps, the probability he'll fall exactly 23 times is $0.72$
Can anyone check if I got the correct results?
EDIT: for some reason when i try to write the full calculations it goes wrong, so i'll explain what i did and which formula i used.
for 1:$C_50,20$ with the given probabilities times $20$ and $30$ accordingly
for 2: using the variance distribution formula along with the given details: $varleft(xright)=binom{n}{k}p^kleft(1-pright)^{n-k}$
for 3: for some reason now i can't find a way to land on $-27$ on the last step(the 50th)
for 4:using the same formula, $c_2000,23$ with 0.1 times 23 and 0.99 times 1977 (calculated using complements(1-p))
probability discrete-mathematics stochastic-processes random-walk
edited Dec 22 '18 at 17:46
Jneven
953322
asked May 1 '18 at 21:15
BeginningMathBeginningMath
59929
$endgroup$
4
$begingroup$
It would be helpful in helping you if you included how you arrived at your answers.
$endgroup$
– Remy
May 1 '18 at 21:18
$begingroup$
I’m assuming that you studying mathematics in at a school or something like that. Here is a hint that will serve you well. Always write down the steps you took from the question to your answer. Even if you got the answer wrong you will still get marks for showing the correct steps.
$endgroup$
– Q the Platypus
May 2 '18 at 0:43
$begingroup$
I'm not even sure I understand what question 3 is asking.
$endgroup$
– Brian Tung
May 2 '18 at 0:57
$begingroup$
i'll edit it and elaborate this post when i'll get back home
$endgroup$
– BeginningMath
May 2 '18 at 20:30
$begingroup$
@Remy && Brian and Q: fixed it and addd explanations. please check andd correct me if i've done something wrong
$endgroup$
– BeginningMath
May 3 '18 at 12:42
add a comment |
$begingroup$
I would appreciate if you could check if I obtained the right results:
The problem:
A drunk man is walking in random steps along an axis with the points +-1, +-2,+-3,... each steps he does is in the length of 1 unit with the probability of 0.4 forward and 0.6 backwards(the steps are undependable). X will mark his placement on the axis after 50 steps.
1. What is $p{x=-10}$
My answer:
The probability that the drunken man will be at position $x=-10$ after 50 steps is $0.053$
2. What is the variance of $x$?
My answer:
Using the binomial variance distribution $varleft(xright)=binom{n}{k}p^kleft(1-pright)^{n-k}$ i obtained that the variance is 24
3. What are the odds that his last step ($50$th) will be at $x = -27$?
My answer:
The odds of his last step, the $50$th, will be at position $x = -27$ is $0.130$
4. Assuming the the chances of the drunken man of falling in each step is $0.01$: if the drunken man walks for $2000$ steps, what are the odds in estimation that he will fall exactly $23$ times?
My answer:
I am quite sure I got this one wrong, but after 2000 steps, the probability he'll fall exactly 23 times is $0.72$
Can anyone check if I got the correct results?
EDIT: for some reason when i try to write the full calculations it goes wrong, so i'll explain what i did and which formula i used.
for 1:$C_50,20$ with the given probabilities times $20$ and $30$ accordingly
for 2: using the variance distribution formula along with the given details: $varleft(xright)=binom{n}{k}p^kleft(1-pright)^{n-k}$
for 3: for some reason now i can't find a way to land on $-27$ on the last step(the 50th)
for 4:using the same formula, $c_2000,23$ with 0.1 times 23 and 0.99 times 1977 (calculated using complements(1-p))
probability discrete-mathematics stochastic-processes random-walk
edited Dec 22 '18 at 17:46
Jneven
953322
asked May 1 '18 at 21:15
BeginningMathBeginningMath
59929
$endgroup$
I would appreciate if you could check if I obtained the right results:
The problem:
A drunk man is walking in random steps along an axis with the points +-1, +-2,+-3,... each steps he does is in the length of 1 unit with the probability of 0.4 forward and 0.6 backwards(the steps are undependable). X will mark his placement on the axis after 50 steps.
1. What is $p{x=-10}$
My answer:
The probability that the drunken man will be at position $x=-10$ after 50 steps is $0.053$
2. What is the variance of $x$?
My answer:
Using the binomial variance distribution $varleft(xright)=binom{n}{k}p^kleft(1-pright)^{n-k}$ i obtained that the variance is 24
3. What are the odds that his last step ($50$th) will be at $x = -27$?
My answer:
The odds of his last step, the $50$th, will be at position $x = -27$ is $0.130$
4. Assuming the the chances of the drunken man of falling in each step is $0.01$: if the drunken man walks for $2000$ steps, what are the odds in estimation that he will fall exactly $23$ times?
My answer:
I am quite sure I got this one wrong, but after 2000 steps, the probability he'll fall exactly 23 times is $0.72$
Can anyone check if I got the correct results?
EDIT: for some reason when i try to write the full calculations it goes wrong, so i'll explain what i did and which formula i used.
for 1:$C_50,20$ with the given probabilities times $20$ and $30$ accordingly
for 2: using the variance distribution formula along with the given details: $varleft(xright)=binom{n}{k}p^kleft(1-pright)^{n-k}$
for 3: for some reason now i can't find a way to land on $-27$ on the last step(the 50th)
for 4:using the same formula, $c_2000,23$ with 0.1 times 23 and 0.99 times 1977 (calculated using complements(1-p))
probability discrete-mathematics stochastic-processes random-walk
probability discrete-mathematics stochastic-processes random-walk
edited Dec 22 '18 at 17:46
Jneven
953322
asked May 1 '18 at 21:15
BeginningMathBeginningMath
59929
edited Dec 22 '18 at 17:46
Jneven
953322
asked May 1 '18 at 21:15
BeginningMathBeginningMath
59929
edited Dec 22 '18 at 17:46
Jneven
953322
edited Dec 22 '18 at 17:46
Jneven
953322
edited Dec 22 '18 at 17:46
Jneven
953322
953322
asked May 1 '18 at 21:15
BeginningMathBeginningMath
59929
asked May 1 '18 at 21:15
BeginningMathBeginningMath
59929
asked May 1 '18 at 21:15
BeginningMathBeginningMath
59929
59929
4
$begingroup$
It would be helpful in helping you if you included how you arrived at your answers.
$endgroup$
– Remy
May 1 '18 at 21:18
$begingroup$
I’m assuming that you studying mathematics in at a school or something like that. Here is a hint that will serve you well. Always write down the steps you took from the question to your answer. Even if you got the answer wrong you will still get marks for showing the correct steps.
$endgroup$
– Q the Platypus
May 2 '18 at 0:43
$begingroup$
I'm not even sure I understand what question 3 is asking.
$endgroup$
– Brian Tung
May 2 '18 at 0:57
$begingroup$
i'll edit it and elaborate this post when i'll get back home
$endgroup$
– BeginningMath
May 2 '18 at 20:30
$begingroup$
@Remy && Brian and Q: fixed it and addd explanations. please check andd correct me if i've done something wrong
$endgroup$
– BeginningMath
May 3 '18 at 12:42
add a comment |
4
$begingroup$
It would be helpful in helping you if you included how you arrived at your answers.
$endgroup$
– Remy
May 1 '18 at 21:18
$begingroup$
I’m assuming that you studying mathematics in at a school or something like that. Here is a hint that will serve you well. Always write down the steps you took from the question to your answer. Even if you got the answer wrong you will still get marks for showing the correct steps.
$endgroup$
– Q the Platypus
May 2 '18 at 0:43
$begingroup$
I'm not even sure I understand what question 3 is asking.
$endgroup$
– Brian Tung
May 2 '18 at 0:57
$begingroup$
i'll edit it and elaborate this post when i'll get back home
$endgroup$
– BeginningMath
May 2 '18 at 20:30
$begingroup$
@Remy && Brian and Q: fixed it and addd explanations. please check andd correct me if i've done something wrong
$endgroup$
– BeginningMath
May 3 '18 at 12:42
4
4
$begingroup$
It would be helpful in helping you if you included how you arrived at your answers.
$endgroup$
– Remy
May 1 '18 at 21:18
$begingroup$
It would be helpful in helping you if you included how you arrived at your answers.
$endgroup$
– Remy
May 1 '18 at 21:18
$begingroup$
I’m assuming that you studying mathematics in at a school or something like that. Here is a hint that will serve you well. Always write down the steps you took from the question to your answer. Even if you got the answer wrong you will still get marks for showing the correct steps.
$endgroup$
– Q the Platypus
May 2 '18 at 0:43
$begingroup$
I’m assuming that you studying mathematics in at a school or something like that. Here is a hint that will serve you well. Always write down the steps you took from the question to your answer. Even if you got the answer wrong you will still get marks for showing the correct steps.
$endgroup$
– Q the Platypus
May 2 '18 at 0:43
$begingroup$
I'm not even sure I understand what question 3 is asking.
$endgroup$
– Brian Tung
May 2 '18 at 0:57
$begingroup$
I'm not even sure I understand what question 3 is asking.
$endgroup$
– Brian Tung
May 2 '18 at 0:57
$begingroup$
i'll edit it and elaborate this post when i'll get back home
$endgroup$
– BeginningMath
May 2 '18 at 20:30
$begingroup$
i'll edit it and elaborate this post when i'll get back home
$endgroup$
– BeginningMath
May 2 '18 at 20:30
$begingroup$
@Remy && Brian and Q: fixed it and addd explanations. please check andd correct me if i've done something wrong
$endgroup$
– BeginningMath
May 3 '18 at 12:42
$begingroup$
@Remy && Brian and Q: fixed it and addd explanations. please check andd correct me if i've done something wrong
$endgroup$
– BeginningMath
May 3 '18 at 12:42
add a comment |
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4
$begingroup$
It would be helpful in helping you if you included how you arrived at your answers.
$endgroup$
– Remy
May 1 '18 at 21:18
$begingroup$
I’m assuming that you studying mathematics in at a school or something like that. Here is a hint that will serve you well. Always write down the steps you took from the question to your answer. Even if you got the answer wrong you will still get marks for showing the correct steps.
$endgroup$
– Q the Platypus
May 2 '18 at 0:43
$begingroup$
I'm not even sure I understand what question 3 is asking.
$endgroup$
– Brian Tung
May 2 '18 at 0:57
$begingroup$
i'll edit it and elaborate this post when i'll get back home
$endgroup$
– BeginningMath
May 2 '18 at 20:30
$begingroup$
@Remy && Brian and Q: fixed it and addd explanations. please check andd correct me if i've done something wrong
$endgroup$
– BeginningMath
May 3 '18 at 12:42