Results 1 to 10 of 10

Math Help - Statistics Probability Distribution..

  1. #1
    Junior Member
    Joined
    May 2007
    Posts
    56

    Smile Statistics Probability Distribution..

    Hey

    I am stuck on this question in the June '04 Edexcel past paper.. I know how to find the answer but I can't get any further so I am stuck.. It's reasonably easy probably.. Here's the question:

    3.
    A discrete random variable X has a probability function as shown in the table below, where a and b are constants

    x - 0, 1, 2, 3
    P(X=x) - 0.2, 0.3, b, a

    Given that E(X) = 1,7,

    (a) Find the value of a and the value of b


    ------------------------

    So far, I have got 2b+3a = 1.4

    Don't know what to do next..

    Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor kalagota's Avatar
    Joined
    Oct 2007
    From
    Taguig City, Philippines
    Posts
    1,026
    i think given your data, you can get the variance.. Var \, X = E[X^2] - E[X]^2
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    May 2007
    Posts
    56
    I know that, but how does that help me in finding a and b? I need to find them and they are constants..
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor kalagota's Avatar
    Joined
    Oct 2007
    From
    Taguig City, Philippines
    Posts
    1,026
    of course your variance is in terms of a and b.. thus you have 2 equations in 2 unknowns..
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Oli
    Oli is offline
    Member
    Joined
    Apr 2008
    Posts
    82
    Writing down the equation for the variance doesn't help, because you don't know what the variance actually is, and so you end up with another unknown.

    The sum of the probabilities must be equal to 1. That is how you get your 2nd equation.

    0.2 + 0.3 + b + a = 1
    So
    b + a = 0.5

    And:
    2a + 3b = 1.4 from what you did.

    These are linearly independent, so solve to find a and b.
    b=0.4
    a=0.1
    Follow Math Help Forum on Facebook and Google+

  6. #6
    GAMMA Mathematics
    colby2152's Avatar
    Joined
    Nov 2007
    From
    Alexandria, VA
    Posts
    1,172
    Awards
    1
    Quote Originally Posted by Danielisew View Post
    Hey

    I am stuck on this question in the June '04 Edexcel past paper.. I know how to find the answer but I can't get any further so I am stuck.. It's reasonably easy probably.. Here's the question:

    3.
    A discrete random variable X has a probability function as shown in the table below, where a and b are constants

    x - 0, 1, 2, 3
    P(X=x) - 0.2, 0.3, b, a

    Given that E(X) = 1,7,

    (a) Find the value of a and the value of b


    ------------------------

    So far, I have got 2b+3a = 1.4

    Don't know what to do next..

    Thanks!
    You will have a system of two equations. The other equation is: b+a=0.5 because all the probabilities must add up to one.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Junior Member
    Joined
    May 2007
    Posts
    56
    Oh yeah stupid me.. THanks for that.
    I did the variance one whilst minusing the E(X) and got the equation:

    2b + 12a = 1.1

    Don't know if that would work too..

    I'll use the obvious one a+b = 0.5
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor kalagota's Avatar
    Joined
    Oct 2007
    From
    Taguig City, Philippines
    Posts
    1,026
    haha.. yeah.. i forgot that thing!
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Junior Member
    Joined
    May 2007
    Posts
    56
    Wait... Guys I am even more stuck and confused now.
    I got a = 0.4 and b = 0.1

    I simultaneously solved :

    2b + 3a = 1.4
    2b + 2a = 1

    Isn't that second one the same as a + b = 0.5 ?

    Anyway.. A later question says show that the variance of X is 1.41, but I can't get that to work lol.. Is Oli right or me with values of a and b? Can you double the equation to give 2b + 2a = 1 ?
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Oli
    Oli is offline
    Member
    Joined
    Apr 2008
    Posts
    82
    You are right, I solved for 2a+3b=1.4. Should have solved for 3a+2b=1.4. My mistake.

    The variance is:
    E(X^2)-E(X)^2
    This is:
    0^2.P(X=0)+(1^2)P(X=1)+(2^2)P(X=2)+(3^2)P(X=3)-E(X)^2
    =1*0.3+4*b+9*a-1.7^2
    =0.3+0.4+3.6-1.7^2
    =4.3-1.7^2
    =1.41
    Last edited by Oli; April 9th 2008 at 07:50 AM. Reason: I made a rather crucial calculation error!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Statistics Sampling Distribution
    Posted in the Statistics Forum
    Replies: 0
    Last Post: December 6th 2011, 11:17 AM
  2. AP Statistics probability - binomial distribution
    Posted in the Statistics Forum
    Replies: 3
    Last Post: December 24th 2009, 08:19 PM
  3. Replies: 1
    Last Post: October 5th 2009, 02:14 AM
  4. help! statistics (normal distribution)
    Posted in the Statistics Forum
    Replies: 2
    Last Post: December 6th 2008, 05:02 PM
  5. Statistics: Joint Probability Distribution Problem
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: October 22nd 2008, 01:28 AM

Search Tags


/mathhelpforum @mathhelpforum