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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Suppose twin brothers, Lim and Jim are taking part in an experiment called ‘Twin’sTelepathy Test’. In this test, 5 candles of different colors are shown to both the brothersin the beginning. Then, the twins are put into two different rooms and the candles aregiven to Jim. He picks a candle himself, presses a buzzer to let Lim know that onecandle’s been picked without telling him the color of the candle. Then Jim tries toconnect to Lim through his mind and transmit the name of the color to Lim telepathically.Now, Lim has to guess the color of the candle. This goes on for 5 times for all fivecandles.a. What is the probability that Lim makes exactly 4 right guesses?b. The same experiment is repeated, but this time after each wrong guess Lim makes,the correct answer is shown to him. Now what is the probability that Lim makesexactly 4 right guesses?
1) Consider an independent sample of size N drawn from the Bernoulli distribution, with probability parameter 0. That is, yi = 1 with probability 0 and zero with probability 1- 0. a) Write down the log likelihood function for the sample and show that the MLE is the sample mean. b) Derive the score and the Hessian (it's a scalar here since there is only one parameter). Derive the information “matrix," which is scalar here. c) Derive the formulas for the Wald and LM tests of the hypothesis that 0= 0o (against the alternative that it's anything else). Verify that under the null the two test statistics have the same probability limit. d) Derive the LR test statistic for the same hypothesis. e) Suppose you draw a sample with 5 observations, all of which are zero. Your prior distribution is uniform. Find the posterior mean and construct a 90% Bayesian coverage area.
4 The probability density Runetron (Pd) of a signal is ginen by ke PCx) = etherwse a) what is the step size (9) if tlrere are 24 quantitatron lenls- b) hmd the vodue f Conslent K
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)?
Suppose that Bag 1 contains 4 red balls and 2 green balls, and Bag 2 contains 3 red balls and 3 greenballs. You draw two balls at random from Bag 1, and two balls at random from Bag 2.(a) Compute the probability that all four balls drawn are the same colour.(b) Compute the probability that all four balls drawn are green given that all four balls drawn are thesame colour.
5. A candy dish contains 2 red (R) and 4 yellow (Y) candies. You close your eyes, select two candies from the dish (without replacement), and record their colors. Use general multiplication rule and special addition rule to find the following probabilities. a. The probability that the first selected candy will be red and the second selected candy will be yellow is b. The probability that two selected candies will be of different colors_ One is red, another one is yellow c. Probability that two selected candies will be of the same color_ Both are red or both are yellow Assuming that the event "The first selected candy will be red and the second selected candy will be yellow "is denoted by A, the event "Two selected candies will be of different colors" is denoted by B, and the event "Two selected candies will be of the same color" is denoted by C, show your work in finding P(A), P(B), and P(C) in the questions a, b, and c.
A production engineer found that a particular manufacturing process Couses defects in 6 of Eight of these Components every 20 Com ponents . are ex amined, what is the probability that at Least two of these components have defe cts?
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!
Suppose there are a million cars made by a car company across the globe, where the probability that a car has a defective brake part is 0.0002. Based on the Monte Carlo algorithm, determine the minimum number of cars that needs to be tested so the probability of finding not even a defective car among those tested is less than two in a million. Use a calculator to simplify your answer and obtain the minimum number of cars.
There are two urns. The first urn has 2 black balls and 1 white ball inside and there are 2 black balls and 2 white balls in the second Urn. You ask your friend to randomly choose an Urn and pick 2 balls one by one with no replacement. 1c) If one black and one white ball are selected, what is the probability that your friend selects the Urn with 3 balls inside? 1d) If we repeat this experiment from the beginning with 5 different friends. What is the probability that 2 of them get 2 black balls? 1e) On average (expected value) how many of those 5 friends will get 2 black balls?
In a three-cylinder engine there are three soark plugs. The engine will continue to work unless all three spark plugs malfunction. There is a 43% chaoce that the first spark piug will malivnction. If the first spark plug malfunctions, the chance that the second one mallunctions is 45%. Further, if the first and second spark piugs both maifunclion, the chance that the last one malfunctions is 47%. What is the probability that the engine wil stop working?
4.9Q) Let P and Q be two random variables such that E(P) =7 and E(Q)= 4, then E(4P+3Q+5) is: 1)42 2)44 3)45 4)38

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