a) A memory less source emit 3 messages according to given probabilities. 0.5 0.4 0.3 0.2 0.1 message1 message2 message3 COMPARE efficiency of ternary Huffman code with its third order extension.

Ex. 17b-Section 4.2, Exercise 17b A k out of n system is one in which there is a group of n components, and the system will function if at least k of the components function. Assume the components function independently of one another. In a 3 out of n system, in which each component has probability 0.4 of functioning, what is the smallest value of n needed so that the probability that the system functions is at least 0.4? Note: Your answer must be a whole number. The smallest value of n needed so that the probability that the system functions is at least 0.4=

A digital communication channel transmits bits of information, usually designated as 0 and 1. If a sender transmits a 0, he/she hopes the recipient receives a 0. If a sender transmits a 1, he/she hopes that the recipient receives a 1. Unfortunately, this is not always the case. Suppose on a certain transmission line, a transmitted 0 is received correctly 90% of the time (10% of the time a 1 is received), and a transmitted 1 is received correctly 74% of the time. (26% of the time a 0 is received.) It is known that on this transmission line, 80% of all bits transmitted are 0 bits.A randomly selected transmitted bit is examined. Say its value is X. The bit received is Y.a.What is the probability that X = 0? b.What is the probability that X = 0 and Y = 0? c. What is the probability that X = 1 and Y = 0? d. What is the probability that Y = 0? e. What is the probability that X = 0 given that Y = 0? f. If 1000 random transmitted bits are examined, what is the expected number of 0 bits in this…

In a Binary Symmetric (Communication) Channel (BSC) data is sent data is sent using bits 0 and 1. Whenthe source and the destination are far apart, there are repeaters that decode the bit and transmit generate asignal. However due to noise, there decoding error, i.e., there a probability α that a bit 0 will be decodedas (and hence transmitted) as 1. Similarly, β is the probability that a bit 1 will be decoded as (and hencetransmitted as) 1. Let X0 be the bit’s initial parity and and let Xn be the bits parity after the nth repeater.1. Construct the one-step transition matrix for this Markov Chain.2. Suppose the input stream to this communication channel consists of 80% 0s and 20% 1s. Determinethe proportion of 0s and 1s after the first repeater.3. Under the same input values as in (b) determine the proportions of 0s and 1s exiting the 5th relay.

56.5

Consider a binary communication system that transmits either a zero or a one with with probability pı and p2 respectively. Transmitting probabilities have a ratio of pi /p2 = 3/4. Because of channel noise, about 5 percent of the time a transmitted zero is received as a one, and 10 percent of time a transmitted one is received as a zero by error. a) Compute the probability of receiving zero. b) Suppose a zero is received, what is the probability that a zero was transmitted? c) Determine the overall error rate of the system.

its is known that 90 % of all personal computer of a particular model will operate for at least 1 year  before needing repair . a manager purchase two of these computers a. find the probablity that both computers will work for at least 1 year before needing repair    b. find the probablity that at least 1 computer will work

SO what would be the L, Lq, and Wq of this problem? Assuming we are trying to develop and sovle a waiting line system that can accomodate this increased leel of passenger traffic.

This student never eats the same kind of food for 2 consecutive weeks. If she eats in a Korean restaurant one week, then she is four times as likely to have Turkish as French food the next week. If she eats in a Turkish restaurant one week, then she is equally likely to have Korean as French food the next week. If she eats in a French restaurant one week, then she is five times as likely to have Korean as Turkish food the next week. Assume that state 1 is Korean and that state 2 is Turkish, and state 3 is French. Find the transition matrix for this Markov process. ... ... P = ... ...

1.) Let arr86 be a binary variable equal to 1 if a man was arrested during 1986, and zerootherwise. You have a dataset of young men from California who were born in 1960 or1961 and have at least one arrest prior to 1986. You also have data on the proportion ofprior arrests that led to a conviction (pcnv), the average sentence served from priorconvictions in months (avgsen), months spent in prison since age 18 prior to 1986(tottime), months spent in prison in 1986 (ptime86), and the number of quarters (0 to 4)that the man was legally employed in 1986 (qemp86). You estimate the following linearprobability model (standard errors are in parentheses): arr86 = 0.441 - .162pcnv + .0061avgsen - .0023tottime              (.017)        (.021)         (.0065)           (.005) - .022ptime86 - .043qemp86 (.005)                (.005) n= 2725R2=.0474 a) Interpret the coefficient on avgsen, commenting on both magnitude and significance. Based on these results, do longer sentences deter future crime?…