any 6 of the following 12 problems.ns from Chapter 4 of your textbook ["Communication Systems", by Simon Haykin and5th edition]: 4.3, 4.5(a), 4.10(a,c,d), 4.22ns from Chapter 51. For the binary symmetric channel discussed in the lecture (example 5.1 ofyour textbook), find P(Ao|Bo), P(A¡|Bo), P(Ao|B1), P(A¡|B1).2. Determine the mean and variance of a random variable uniformly dis-tributed in [a, b].3. Let X be a random variable with mean µx and variance oz. Let Y(X – µx)/ox. Determine mean and variance of Y.4. Consider a random variable X having a probability density function fx(x) =aexp(-b|x|), ∞ < x < ∞, where a and b are real constants.(a) Find the condition(s) on a and b so that the probability densityfunction is valid.(b) Determine the probability distribution function of X 1/2(c) Find the probability that the random variable X lies between 12, that is, P(1 < X < 2).5. Consider the random experiment of selecting a number uniformly dis-tributed over the range {1,2,3, ..., 120}. Let A, B,C be the events thatthe selected number is a multiple of 3, 4, and 6 respectively. Determine:P(A), P(B), P(An B), P(AU B), P(AnC)6. Consider a message packet that is 10 bits long.(a) How many such messages are possible?(b) How many messages contain exactly 4 ones?(c) Suppose 10th bit is not independent and is chosen such that modulo-2 sum of all the bits is zero. This is called even parity sequence. Howmany such even parity sequences are possible?(d) If the even parity sequence is transmitted over a channel that hasprobability of error p for each bit (independent of others). What isthe probability that the received sequence has an undetected error?7. The probability that an event occur at least once in four indeper Ris equal to q. What is the probability of occurrence of the evtrial. You are given that the probabilities are equal in all trials.8. Exponential probability density function is given by fr (7) = 1/Xexp(-1/)for T > 0; and fT(T) = 0, for 7 < 0. Determine the mean and variance oТ.

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2. Determine the mean and variance of a random variable uniformly dis- tributed in [a, b].

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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