Homework had this question. Part a is relatively straightforward, as it's a cdf of the function. For part b I could write a script that will compute all possible sets and divide by the total sets, but how would I solve this problem in an efficient way?
A binary communication channel transmits a sequence of "bits" (0s and 1s). Suppose that for any particular bit transmitted, there is a 15% chance of a transmission error (a 0 becoming a 1 or a 1 becoming a 0). Assume that bit errors occur independently of one another. (Round your answers to four decimal places.)
(a)
Consider transmitting 1000 bits. What is the approximate probability that at most 175 transmission errors occur?
.9868
Correct: Your answer is correct.
(b)
Suppose the same 1000-bit message is sent two different times independently of one another. What is the approximate probability that the number of errors in the first transmission is within 60 of the number of errors in the second?
Best Answer
As answered by @Ragib Zaman, I have to use the central limit theorem to calculate the answer instead of treating it as a binomial answer).