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Probability Question (Random Variables and CDF)

  • Thread starter swuster
  • Start date
  • #1
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Homework Statement


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?

Homework Equations


n/a


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?
 

Answers and Replies

  • #2
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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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