How to find probability











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Consider this question:



Mean of $X$ is 20 and upper bound is 50. If $X$ changes daily with mean 0 and variance 1, independently of the other days. If today $X=40$ what can you say about the probability that $X$ will be between 35 and 45 after 5 days.
ChebyChev is supposed to be used for this. I am unsure of how to use it. If the mean is 20 and the value is 40 then tomorrow mean will be 20 and variance would be increased by 1. So, whatever variance is today it will be 5 times, 5 days from now. So, P(35 <= X <= 45) = P(X - 20 >= 5*var) = 1/25.
Is this correct?










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  • "Looks like standard normal RV" Yes, somehow it does. But it is not mentioned in the text.
    – callculus
    Nov 15 at 17:18










  • Can I solve it using ChebyChev or Chernoff? What would be the steps taken further?
    – puffles
    Nov 16 at 6:20

















up vote
0
down vote

favorite












Consider this question:



Mean of $X$ is 20 and upper bound is 50. If $X$ changes daily with mean 0 and variance 1, independently of the other days. If today $X=40$ what can you say about the probability that $X$ will be between 35 and 45 after 5 days.
ChebyChev is supposed to be used for this. I am unsure of how to use it. If the mean is 20 and the value is 40 then tomorrow mean will be 20 and variance would be increased by 1. So, whatever variance is today it will be 5 times, 5 days from now. So, P(35 <= X <= 45) = P(X - 20 >= 5*var) = 1/25.
Is this correct?










share|cite|improve this question

















This question has an open bounty worth +50
reputation from puffles ending in 3 days.


Looking for an answer drawing from credible and/or official sources.
















  • "Looks like standard normal RV" Yes, somehow it does. But it is not mentioned in the text.
    – callculus
    Nov 15 at 17:18










  • Can I solve it using ChebyChev or Chernoff? What would be the steps taken further?
    – puffles
    Nov 16 at 6:20















up vote
0
down vote

favorite









up vote
0
down vote

favorite











Consider this question:



Mean of $X$ is 20 and upper bound is 50. If $X$ changes daily with mean 0 and variance 1, independently of the other days. If today $X=40$ what can you say about the probability that $X$ will be between 35 and 45 after 5 days.
ChebyChev is supposed to be used for this. I am unsure of how to use it. If the mean is 20 and the value is 40 then tomorrow mean will be 20 and variance would be increased by 1. So, whatever variance is today it will be 5 times, 5 days from now. So, P(35 <= X <= 45) = P(X - 20 >= 5*var) = 1/25.
Is this correct?










share|cite|improve this question















Consider this question:



Mean of $X$ is 20 and upper bound is 50. If $X$ changes daily with mean 0 and variance 1, independently of the other days. If today $X=40$ what can you say about the probability that $X$ will be between 35 and 45 after 5 days.
ChebyChev is supposed to be used for this. I am unsure of how to use it. If the mean is 20 and the value is 40 then tomorrow mean will be 20 and variance would be increased by 1. So, whatever variance is today it will be 5 times, 5 days from now. So, P(35 <= X <= 45) = P(X - 20 >= 5*var) = 1/25.
Is this correct?







probability probability-theory






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edited Nov 18 at 10:24

























asked Nov 15 at 16:27









puffles

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This question has an open bounty worth +50
reputation from puffles ending in 3 days.


Looking for an answer drawing from credible and/or official sources.








This question has an open bounty worth +50
reputation from puffles ending in 3 days.


Looking for an answer drawing from credible and/or official sources.














  • "Looks like standard normal RV" Yes, somehow it does. But it is not mentioned in the text.
    – callculus
    Nov 15 at 17:18










  • Can I solve it using ChebyChev or Chernoff? What would be the steps taken further?
    – puffles
    Nov 16 at 6:20




















  • "Looks like standard normal RV" Yes, somehow it does. But it is not mentioned in the text.
    – callculus
    Nov 15 at 17:18










  • Can I solve it using ChebyChev or Chernoff? What would be the steps taken further?
    – puffles
    Nov 16 at 6:20


















"Looks like standard normal RV" Yes, somehow it does. But it is not mentioned in the text.
– callculus
Nov 15 at 17:18




"Looks like standard normal RV" Yes, somehow it does. But it is not mentioned in the text.
– callculus
Nov 15 at 17:18












Can I solve it using ChebyChev or Chernoff? What would be the steps taken further?
– puffles
Nov 16 at 6:20






Can I solve it using ChebyChev or Chernoff? What would be the steps taken further?
– puffles
Nov 16 at 6:20












2 Answers
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0
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Well, I think this question want you to point out that the probability of X = 40 in today does not affect the probability of X in the next 5 days. Because it is independently of the other days.



So, if the distribution of X is standard normal distribution, then you can compute the $P(35<=X<=45)$ directly.






share|cite|improve this answer








New contributor




AnNg is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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  • The changes from day to day are independent, which does not make the values on each day independent.
    – wnoise
    Nov 15 at 18:41










  • Do you think it canbe solved using any inequality (Markov, chebychev, chernoff)
    – puffles
    Nov 16 at 6:20


















up vote
0
down vote













The sum of independent Gaussian RVs is a Gaussian RV with a variance that is the sum of the individual variances, and a mean that is the sum of the means. From this, the PDF of values on the last day is immediately available.






share|cite|improve this answer





















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    2 Answers
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    2 Answers
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    up vote
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    down vote













    Well, I think this question want you to point out that the probability of X = 40 in today does not affect the probability of X in the next 5 days. Because it is independently of the other days.



    So, if the distribution of X is standard normal distribution, then you can compute the $P(35<=X<=45)$ directly.






    share|cite|improve this answer








    New contributor




    AnNg is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
    Check out our Code of Conduct.


















    • The changes from day to day are independent, which does not make the values on each day independent.
      – wnoise
      Nov 15 at 18:41










    • Do you think it canbe solved using any inequality (Markov, chebychev, chernoff)
      – puffles
      Nov 16 at 6:20















    up vote
    0
    down vote













    Well, I think this question want you to point out that the probability of X = 40 in today does not affect the probability of X in the next 5 days. Because it is independently of the other days.



    So, if the distribution of X is standard normal distribution, then you can compute the $P(35<=X<=45)$ directly.






    share|cite|improve this answer








    New contributor




    AnNg is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
    Check out our Code of Conduct.


















    • The changes from day to day are independent, which does not make the values on each day independent.
      – wnoise
      Nov 15 at 18:41










    • Do you think it canbe solved using any inequality (Markov, chebychev, chernoff)
      – puffles
      Nov 16 at 6:20













    up vote
    0
    down vote










    up vote
    0
    down vote









    Well, I think this question want you to point out that the probability of X = 40 in today does not affect the probability of X in the next 5 days. Because it is independently of the other days.



    So, if the distribution of X is standard normal distribution, then you can compute the $P(35<=X<=45)$ directly.






    share|cite|improve this answer








    New contributor




    AnNg is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
    Check out our Code of Conduct.









    Well, I think this question want you to point out that the probability of X = 40 in today does not affect the probability of X in the next 5 days. Because it is independently of the other days.



    So, if the distribution of X is standard normal distribution, then you can compute the $P(35<=X<=45)$ directly.







    share|cite|improve this answer








    New contributor




    AnNg is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
    Check out our Code of Conduct.









    share|cite|improve this answer



    share|cite|improve this answer






    New contributor




    AnNg is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
    Check out our Code of Conduct.









    answered Nov 15 at 18:16









    AnNg

    375




    375




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    AnNg is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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    AnNg is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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    • The changes from day to day are independent, which does not make the values on each day independent.
      – wnoise
      Nov 15 at 18:41










    • Do you think it canbe solved using any inequality (Markov, chebychev, chernoff)
      – puffles
      Nov 16 at 6:20


















    • The changes from day to day are independent, which does not make the values on each day independent.
      – wnoise
      Nov 15 at 18:41










    • Do you think it canbe solved using any inequality (Markov, chebychev, chernoff)
      – puffles
      Nov 16 at 6:20
















    The changes from day to day are independent, which does not make the values on each day independent.
    – wnoise
    Nov 15 at 18:41




    The changes from day to day are independent, which does not make the values on each day independent.
    – wnoise
    Nov 15 at 18:41












    Do you think it canbe solved using any inequality (Markov, chebychev, chernoff)
    – puffles
    Nov 16 at 6:20




    Do you think it canbe solved using any inequality (Markov, chebychev, chernoff)
    – puffles
    Nov 16 at 6:20










    up vote
    0
    down vote













    The sum of independent Gaussian RVs is a Gaussian RV with a variance that is the sum of the individual variances, and a mean that is the sum of the means. From this, the PDF of values on the last day is immediately available.






    share|cite|improve this answer

























      up vote
      0
      down vote













      The sum of independent Gaussian RVs is a Gaussian RV with a variance that is the sum of the individual variances, and a mean that is the sum of the means. From this, the PDF of values on the last day is immediately available.






      share|cite|improve this answer























        up vote
        0
        down vote










        up vote
        0
        down vote









        The sum of independent Gaussian RVs is a Gaussian RV with a variance that is the sum of the individual variances, and a mean that is the sum of the means. From this, the PDF of values on the last day is immediately available.






        share|cite|improve this answer












        The sum of independent Gaussian RVs is a Gaussian RV with a variance that is the sum of the individual variances, and a mean that is the sum of the means. From this, the PDF of values on the last day is immediately available.







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Nov 15 at 18:43









        wnoise

        1,4331017




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