Suppose a random variable has m values with probabilities pi > p2 2·2 Pm (m > 100) Prove that for any ternary Huffman code, if the most probable outcome has probability PI < .. 1/31, then that outcome must be assigned a codeword of length at least 2.

Suppose a random variable has m values with probabilities pi > p2 2·2 Pm (m > 100) Prove that for any ternary Huffman code, if the most probable outcome has probability PI < .. 1/31, then that outcome must be assigned a codeword of length at least 2.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

In a digital communication channel, assume that the number of bits received in error can be modeled by a binomial random variable, and assume that the probability that a bit is received in error is 0.0001. If 150,000 bits are transmitted, what is the probability that errors are between 10 and 18? How to compute P(X=10)= (150000c10)(0.0001)10(1-0.0001)150000-10
A QR code photographed in poor lighting, so that it can be difficult to distinguish black and white pixels. The gray color (X) in each pixel is therefore coded on a scale from 0 (white) to 100 (black). The true pixel value (without shadow) the code is Y = 0 for white, and Y = 1 for black. We treat X and Y as random variables. For the highlighted pixel in the figure is the gray color X = 20 and the true pixel value is white, i.e. Y = 0. We assume that QR codes are designed so that, on average, there are as many white as black pixels, which means that pY (0) = pY (1) = 1/2. In this situation, X is continuously distributed (0 ≤ X ≤ 100) and Y is discretely distributed, but we can still think about the simultaneous distribution of X and Y. We start by defining the conditional density of X, given the value of Y : fX|Y(x|0) = "Pixel is really white" fX|Y(x|1) =" Pixel is really balck " Use Bayes formula as given in the picture and find the probability for x = 20 like in the picture.
Assume that random guesses are made for 8 multiple-choice questions on a test with 5 choices for each question, so that there are n=8 trials, each with probability of success (correct) given by p=0.20. Find the probability of no correct answers.
Suppose that the number of emergency patients in a given day at a certain hospital is a Poisson random variable X with parameter20. What is the probability that in a given day there will be at most 5 emergency patients?
Find the probability that a lot of 100 items, of which five are defective, will be accepted in a test of a randomly selected sample containing half the lot if, to be accepted, the number of defective items in a lot of 50 cannot exceed one.
The finish of a hole depends on the edge of the bit used, only 1% of the holes with a new drill have an irregular cut, 3% have an irregular cut with average bits and 5% present irregular cut with worn bits. If 25% of the holes are made with new bits, 60% have average edges and 15% are worn out. [use 3 decimal places] a) If a piece is taken at random, what is the probability of having holes irregular? b) If a piece with irregular holes is taken, what is the probability that would have been made with an average drill bit?
Assume that random guesses are made for eight multiple choice questions on an SAT test, so that there are n=8 trials, each with probability of success (correct) given by p=0.5. Find the indicated probability for the number of correct answers. Find the probability that the number x of correct answers is fewer than 4. P(X<4)= ive been trying to figure this out for over an hour
Which one of the following is not a true for the Negative Binomial distribution ? a) The random variable can start at y =0 b) The trials in the experiment are independent c) The negative binomial distribution parameters are the number of successes and the probability of a success d) The random variable denotes the number of failures that occured until the rth success is obtained e) There are only two outcomes, a success and a failure
What is the probability that three Poisson random independent variables A,B, C, with parameters 1, 1, 9, respectively are all equal? The answer needs to be expressed as an infinite sum of exponentials and factorials.
(b) Test two independent circuits one after the other. On each test, the possible outcome is either overvoltage (0) or undervoltage (U). Assume that all circuits are overvoltage with probability 0.4. Let X be the number of overvoltage circuit in the first test and Y be the number of overvoltage circuit before you observed undervoltage. If both circuit is overvoltage or undervoltage, Y = 2. Find the joint PMF of X and Y.
Of 9 randomly selected male students, Xj used Apple computer, whereas of 12 randomly selected female student, X2 used Apple computer. Let: p1 and p2 denote the probabilities that a randomly selected male and female students, respectively, played tennis. what is unbiased estimator of P1 - P2 ? X2 Da. 7+ 12 X1 X2 Ob. 49 144 X2 12 X1 Od. 49 X2 144
There are three very old X-ray security machines in the departure complex of an airport. All three machines are exactly the same. The probability that a machine breaks down in the course of a day is 0.2. If they are all in working order at the beginning of a day, and breakdowns are independent of each other, find the probability that during the day: use binomial – success or failure(a) there are no breakdowns=0.512 =3C0*.20*.83(b) one machine breaks down=0.384=3C1*.21*.82(c) two machines break down=0.096=3C2*.22*.81(d) all three machines break down=0.008=3C3*.23*.80