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Each bit transmitted through a channel has a 10% chance to be transmitted in error. Assume that the bits are transmitted independently. Let X denote the number of bits in error in the next 18 transmitted bits. Answer the following questions a) Find the probability that in the next 18 transmitted bits, at least 3 transmitted in error. b) Calculate the expected value, variance and standard deviation of X. c) Find the probability that X is within 1 standard deviation of its mean value.

Each bit transmitted through a channel has a 10% chance to be transmitted in error. Assume that the bits are transmitted independently. Let X denote the number of bits in error in the next 18 transmitted bits. Answer the following questions a) Find the probability that in the next 18 transmitted bits, at least 3 transmitted in error. b) Calculate the expected value, variance and standard deviation of X. c) Find the probability that X is within 1 standard deviation of its mean value.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 31E
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Each bit transmitted through a channel has a 10% chance to be transmitted in error. Assume that the bits are transmitted independently. Let X denote the number of bits in error in the next 18 transmitted bits. Answer the following questions a) Find the probability that in the next 18 transmitted bits, at least 3 transmitted in error. b) Calculate the expected value, variance and standard deviation of X. c) Find the probability that X is within 1 standard deviation of its mean value.
Transcribed Image Text:Each bit transmitted through a channel has a 10% chance to be transmitted in error. Assume that the bits are transmitted independently. Let X denote the number of bits in error in the next 18 transmitted bits. Answer the following questions a) Find the probability that in the next 18 transmitted bits, at least 3 transmitted in error. b) Calculate the expected value, variance and standard deviation of X. c) Find the probability that X is within 1 standard deviation of its mean value.
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