soln3 - ECE320 Solution Notes to Homework 3 Spring 2006...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ECE320 Solution Notes to Homework 3 Spring 2006 Cornell University T.L.Fine 1. The average current emitted by a cathode is I amps (coulombs/sec.). The charge emitted over time T seconds is Q coulombs, where a coulomb is approximately (but assume it to be exactly) 6 × 10 18 electrons. (a) If I is one nanoampere and T is one nanosecond then what is the average number of electrons emitted in this time? The average charge is 10- 9 × 10- 9 × 6 × 10 18 = 6 electrons. (b) What is the probability that no electrons will be seen in this time? Use Poisson with mean of 6 to determine P ( K = 0) = e- λ = e- 6 . (c) What is the probability that 2 electrons will be seen in this time? P ( K = 2) = e- 6 6 2 2! = 18 e- 6 . (d) By examining the ratio of probabilities, is seeing 7 electrons more probable than seeing 6 electrons? P ( K = 7) P ( K = 6) = 6 7 7! ÷ 6 6 6! = 6 7 < 1 . Hence, seeing 7 electrons is less probable than seeing 6. 2. Let 10- 2 be the probability of error per bit transmitted in a digital commu- nication system, and let there be 1000 bits in a packet. (a) What is the average number of errors made in transmitting a packet? Bi- nomial B (1000 ,. 01) and EK = np = 1000 × . 01 = 10. (a) Are 100 errors more probable than 101 errors? P ( K = 100) P ( K = 101) = 1000 100 p 100 (1- p ) 900 ÷ 1000 101 p 101 (1- p ) 899 = 101!899! 100!900! 1- p p = 101 900 1- p p = 101(1- . 01) 9 > 1 . Therefore, seeing 100 errors is much more probable than seeing 101 errors....
View Full Document

This homework help was uploaded on 09/25/2007 for the course ECE 3200 taught by Professor Fine during the Spring '06 term at Cornell.

Page1 / 5

soln3 - ECE320 Solution Notes to Homework 3 Spring 2006...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online