4. Two boxes each produce a stream of qubits. Box A produces the qubits all in the state|+) = (10) + |1)). Box B randomly produces qubits in states |0) and |1) , each withprobability 1/2. We have one of the boxes, but it is unmarked and so we do not knowwhich kind it is. Describe an experiment on the qubits that can tell the difference betweenbox A and box B. Can you reliably tell the difference between the boxes by examiningonly one of the qubits?

In quantum computing, a qubit or quantum bit is the basic unit of quantum information- the quantum…

Answered: 4. Two boxes each produce a stream of…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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PM)- Google Chrome va.edu.om/mod/quiz/attempt.php?attempt=818373&cmid%3D121611&page=D5 تجامعتگروی University of Nizwa A coin is tossed four times. The probability of getting more than one tail is OA. 5/8 OB. 11/16 OC. 5/16 OD. 3/8 OE. None of these The probability of getting minimum three heads is Oa. 1/4 Cb.3/4 Oc. 5/16 Cd. 3/8, CE. None of these page
Consider two individuals (1 and 2) and assume their preferences over gamblesover [0, infinity) can be represented respectively by U1 (p) = Sigma p (ai) multiply by squareroot of (ai) and U2 (p) = Sigma p (ai) multiply by exponential of (ai), where p(ai) is the probability p assigns to (ai). Are the two individuals risk-averse, risk-loving or risk-neutral? Compute the Arrow-Pratt measure of absolute risk aversion for the twoindividuals? Compute the certainty equilvalent for the two agents for the gamble thatpays 0 with probability 1/2and 3 with probability 1/2What is the expected value of this lottery? What can you say about the comparison betweenthe expected value and the certainty equivalent (this quantity is calledrisk premium)?
A bin of 5 transistors is known to contain 2 that are defective. The transistors are to be tested, one at a time, until the defective ones are identified. Denote by N1 the number of tests made until the first defective is identified and by N2 the number of additional tests until the second defective is identified. Find the joint probability mass func- tion of N1 and N2.
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.
#28- It is equally probable that the pointer on the spinner shown will land on any one of the eight regions, numbered 1 through 8. If the pointer lands on a borderline, spin again. Find the probability that the pointer will stop on an even number or a number less than 5
There are 33 natural numbers. Prove that you can choose several numbers between them, so that their sum is divisible by three and eleven.It should be possible to solve the problem by the Dirichlet's principe. I can solve it when i choose for exmaple two random numbers(ai, aj): So I can write: 3/(ai-aj) AND 11/(ai-aj)But cant figure out the solution for not specified quantity of numbers.I would ask for a detailed solution, so i can understand the topic and difference. Thanks!
6. A smoke detector system uses two devices, an ionization sensor and a photoelectric sensor. If smoke is present, the probability that it will be detected by the ionization sensor (I) is 0.90, by the photoelectric sensor (P), 0.80, and by both devices, 0.72. a) Draw a Venn diagram to represent the problem. b) If smoke is present, determine the probability that the smoke will be detected by the system. c) if smoke is present, determine the probability that the smoke is undetected. d) are the two alarms operating independently. Justify your answer with a calculation.
5. a) Suppose you have three coins in a bag: the first coin is fair, with prob- ability of HEAD (H) equals to that of TAIL (T), i.e., P(X = H|M1) = P(X = T|M1), where X is a binary random variable representing HEAD or TAIL. The second is a loaded coin with P(X = takes a coin out of the bag at random and flips it. When it lands, you observe that the side of the coin facing up is HEAD. What is the probabilities that this is the first, second and third coin? Hint: You may assume the three coins are equal likely to be selected from the bag, i.e., P(M1) = P(M2) = P(M3) = , and you need to calculate P(M||X = H), P(M2|X = H) and P(M3|X = H). H|M2) = 0.8. The third is also a loaded coin with P(X = Н Мз) — 0.2. Your friend 6) What if we don't know the probabilities of HEAD for each coin? Design an iterative algorithm using pseudo-code to estimate these probabilities.
13-7. What is the expected number of heads appearing when a fair coin is tossed three 3-28) es Co times
5) A Professor conducts an exam in a class with 24 boys and 16 girls. 6 boys and 4 girls make an A in the course. a) Write the joint pohahility matrix of the gender of the student and his/her grade (A or no A). b) Find the marignal probabilities of a student being a boy or a girl and the marginal probabilities of a student making or not making an A in the course. Show that the gender of a student and whether he/she makes an A in the course, are independent.

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