Results 1 to 4 of 4

Math Help - Digital Communication Question - Conditional Probability

  1. #1
    Junior Member Hasan1's Avatar
    Joined
    Dec 2007
    Posts
    27

    Digital Communication Question - Conditional Probability

    A digital communications system consists of a transmitter and a reciever. During each short transmission interval the transmitter sends a signal which is to be interpreted by a zero, or it sends a different signal which is to be interpreted as a one. At the end of each interval the reciver makes the best guess at that was transmitted. Consider the events:

    T0 = {Transmitter sends 0}
    T1 = {Transmitter sends 1}
    R0 = {Receiver concludes that a 0 was sent}
    R1 = {Reciever concludes that a 1 was sent}

    Assume that P(R0|T0) = 0.99, P(R1|T1) = 0.98 and P(T1) = 0.5

    Find
    a) the probability of a transmission error given R1?
    b) the overall probability of a transmission error
    c) repeat a) and b) assuming P(T1) = 0.8 instead of 0.5
    What I really need to know is how to do a)

    I started off by calculating P(T0) = 1 - P(T1)
    then I wanted to use the formula

    P(T0|R1) = P(T0*R1)/P(R1) [* = intersect]

    I calculated the numerator as P(T0*R1) = P(T0)P(R1|T0)

    and P(R1|T0) = 1 - P(R0|T0)

    but how do I calculate P(R1)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,966
    Thanks
    1785
    Awards
    1
    P(R_1)=P(R_1\cap T_0)+P(R_1\cap T_1)=P(R_1|T_0)P(T_0)+P(R_1|T_1)P(T_1)
    Last edited by Plato; January 31st 2010 at 01:20 PM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member Hasan1's Avatar
    Joined
    Dec 2007
    Posts
    27
    P(R_1\cap T_0)+P(R_1\cap T_1)=P(R_1|T_0)P(T_0)+P(R_1|T_0)P(T_0)

    I understand the first part of your equivalence but is this part a typo?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,966
    Thanks
    1785
    Awards
    1
    Quote Originally Posted by Hasan1 View Post
    P(R_1\cap T_0)+P(R_1\cap T_1)=P(R_1|T_0)P(T_0)+P(R_1|T_1)P(T_1)

    I understand the first part of your equivalence but is this part a typo?
    Indeed there was. It is correct now.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: July 22nd 2011, 02:39 AM
  2. Conditional probability question help
    Posted in the Algebra Forum
    Replies: 4
    Last Post: November 9th 2010, 10:08 AM
  3. Conditional Probability Question
    Posted in the Advanced Statistics Forum
    Replies: 4
    Last Post: February 7th 2010, 08:12 AM
  4. Conditional Probability question
    Posted in the Statistics Forum
    Replies: 1
    Last Post: January 22nd 2010, 08:47 AM
  5. Conditional Probability Question
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: October 5th 2009, 10:16 AM

Search Tags


/mathhelpforum @mathhelpforum