Results 1 to 5 of 5

Math Help - Continuous random variables

  1. #1
    Newbie
    Joined
    Jul 2006
    Posts
    3

    Continuous random variables

    Hi, I have this math assignment on continuous random variables and would greatly appreciate some help. This is the question that I am having trouble with:

    Sara loves shoes and buys many pairs, but gets tired of them quickly. She throughs them away by the pair only into a dumpster, which is emptied every 3 months. Let X be the number of shoes in the dumpster at any given time and let Y be a continuous random variable which is known to be a good approximation of X.

    (a.) whats the numerical value of Pr[X=9] ?
    (b.) Find an expression in terms of Y for each of the following:

    (i) Pr[X=40] (ii) Pr[X<40] (iii) Pr[X>36]

    (c.) If Pr[Y>21] = 1-Pr[X<k], what is the value of k?

    Thanks!!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by rebeccajm
    Hi, I have this math assignment on continuous random variables and would greatly appreciate some help. This is the question that I am having trouble with:

    Sara loves shoes and buys many pairs, but gets tired of them quickly. She throughs them away by the pair only into a dumpster, which is emptied every 3 months. Let X be the number of shoes in the dumpster at any given time and let Y be a continuous random variable which is known to be a good approximation of X.

    (a.) whats the numerical value of Pr[X=9] ?
    As the shoes are thrown out in pairs there will always be an even
    number of shoes in the dumpster so Pr[X=9]=0.

    (b.) Find an expression in terms of Y for each of the following:

    (i) Pr[X=40] (ii) Pr[X<40] (iii) Pr[X>36]

    (c.) If Pr[Y>21] = 1-Pr[X<k], what is the value of k?

    Thanks!!
    To do these last parts we need to know what you know
    about the description of probabilities of continuous random variables.

    Are you familiar with the distribution function (aka the cumulative distribution)?
    Or the probability density function?

    RonL
    the
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jul 2006
    Posts
    3
    I am slightly familiar with the cumulative distribution function. I have done a question which involved making a chart and graphing both the probability distribution fumction as well as the cummulative distribution function. As far as how to use it in this particular question, I am pretty lost. Thanks for your help!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by rebeccajm

    (b.) Find an expression in terms of Y for each of the following:

    (i) Pr[X=40] (ii) Pr[X<40] (iii) Pr[X>36]
    Let Q(y)=Pr(Y<y) be the cumulative probability function for
    the random variable Y Then as Y is a good approximation for
    X we would usualy use the approximation:

    <br />
Pr(X=40) \approx Pr(39.5<Y<40.5)=Q(40.5)-Q(39.5)<br />

    However there is a complication here in that the probability that X
    take an odd value is 0, so to maintain proper nomalisation of
    the probabilities our approximation should probably be:

    <br />
Pr(X=40) \approx Pr(39<Y<41)=Q(41)-Q(39)<br />

    Continuing in this manner we have:

    <br />
Pr(X<40)\approx Pr(Y<39)=Q(39)<br />
,

    and:

    <br />
Pr(X>36)\approx Pr(Y>37)= 1-Pr(Y \le 37)=1-Pr(Y < 37)=1-Q(37)<br />

    (we are using the result that Pr(Y<37)=Pr(Y \le 37) for a continuous RV)

    RonL
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by rebeccajm
    (c.) If Pr[Y>21] = 1-Pr[X<k], what is the value of k?
    The way we have been working, if k is even:

    Pr(X<k) \approx Pr(Y<(k-1)),

    so:

    Pr(Y>21) = 1-Pr(Y<21) \approx 1-Pr(X<22)

    Hence k=22.

    RonL
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Help - continuous random variables...
    Posted in the Statistics Forum
    Replies: 1
    Last Post: April 12th 2010, 11:25 PM
  2. Continuous Random Variables
    Posted in the Statistics Forum
    Replies: 2
    Last Post: November 1st 2009, 11:14 PM
  3. continuous random variables
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: October 20th 2009, 03:19 AM
  4. Continuous random variables
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: January 22nd 2009, 07:30 AM
  5. continuous random variables
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: May 21st 2006, 11:00 AM

Search Tags


/mathhelpforum @mathhelpforum