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Homework Help: Probability Question (Random Variables and CDF)

  1. Feb 23, 2010 #1
    1. The problem statement, all variables and given/known data
    A transmission channel is noisy and a binary bit (assume it is a 0 or a 1) has probability of .11 of being incorrectly transmitted. Suppose the bit is sent n (odd) times and a majority decoder announces which bit is received the majority of the time. Assume retransmissions constitute Bernoulli trials.
    (a) Let X be the number of errors in n transmissions. Give a formula for the distribution of X.
    (b) What is the probability the message is correctly received, for n=25?

    2. Relevant equations
    n/a


    3. The attempt at a solution
    X is discrete, so for part (a) I came up with [tex]p_{x}(x)=.11^{x}.89^{n-x}[/tex] which I'm not convinced is totally right.

    For part b I want to calculate [tex]P(X\leq12)[/tex] since this is the probability that the message is correctly received (number of errors is less than half). But if I attempt to calculate the cumulative distribution function using my distribution, I get [tex]\sum^{12}_{x=1}.11^{x}.89^{n-x} = .06195[/tex] which is clearly way too low. Any help?
     
  2. jcsd
  3. Feb 23, 2010 #2
    hmm, I really confused with the words (my english fault). anyway, what i know about bernoulli's trial is that there's only chance of sucess and failure..

    So, the equation of bernoulli's trial f(x)=(p)x(1-p)1-x , x=0,1

    so, in this case,
    f(x)=(nCx)(0.11)x(0.89)n-x , x=1,2,...,n

    because of n times,
     
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