statistics

The number of independent errors in a transmitted message of n symbols follows a Binomial distribution. The probability of an error in transmission is .001. If 2,000 symbols were sent,
a) Find the expected number of errors.
b) Write out the formula for the distribution of errors in a 2000 symbol message.
c) Find the probability of an error-free message.
d) Find the probability of exactly 1 error.
e) Find the probability of at least 1 error.

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1. p=.001, n=2000
a)Expected number of errors=np=2
b)P(k)=2000Ck*.001^k*.999^(2000-k)
c)P(0)=.999^2000
d)P(1)=2000*.001*.999^1999
e)P(k>=1)=1-P(0)

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