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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?