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... Q1) Given that two events A1 and A2 are statistically independent, show that a) A1 is independent of A2 Q2)A production line manufacturer 5-gal(18.93-liter) gasoline cans to a volume tolerance of 5%. The probability of any one can being out of tolerance is 0.03. if four cans are selected at random: ...
... Q1) Given that two events A1 and A2 are statistically independent, show that a) A1 is independent of A2 Q2)A production line manufacturer 5-gal(18.93-liter) gasoline cans to a volume tolerance of 5%. The probability of any one can being out of tolerance is 0.03. if four cans are selected at random: ...
Probability and statistics
... Probability is not only a tool for us to understand experiments with uncertain outcomes, but also a useful tool in solving problems in the areas closely related to our life. when a life insurance company sells a life insurance policy to a person, the insurance company must determine the fair amount ...
... Probability is not only a tool for us to understand experiments with uncertain outcomes, but also a useful tool in solving problems in the areas closely related to our life. when a life insurance company sells a life insurance policy to a person, the insurance company must determine the fair amount ...
lecture 19 (zipped power point) (update: 13Jan 04)
... More quantitatively, Probability for a particle to be found between point a and b is b ...
... More quantitatively, Probability for a particle to be found between point a and b is b ...
REVIEW OF WAVE MECHANICS
... profoundly disturb the state of a system. If the initial wave function of a system is described as a linear superposition of the eigenfunctions before the measurement, after the measurement it has been “reduced” or “collapsed” to one eigenfunction (assuming that we have performed a perfect ‘noise-fr ...
... profoundly disturb the state of a system. If the initial wave function of a system is described as a linear superposition of the eigenfunctions before the measurement, after the measurement it has been “reduced” or “collapsed” to one eigenfunction (assuming that we have performed a perfect ‘noise-fr ...
Lecture 34: The `Density Operator
... prepare a system in a known initial state, make the measurement, then re-prepare the same initial state and make the same measurement after the same evolution time. With enough repetitions, the results ...
... prepare a system in a known initial state, make the measurement, then re-prepare the same initial state and make the same measurement after the same evolution time. With enough repetitions, the results ...
PHYS6520 Quantum Mechanics II Spring 2013 HW #5
... initial state is a plane wave coming from the left, that is φ(x) ≡ �x|i� = eikx / 2π ...
... initial state is a plane wave coming from the left, that is φ(x) ≡ �x|i� = eikx / 2π ...
Exercise 1, from the final exam in AST4220, 2005 Exercise 2
... The wave function of the Universe gives the probability density for observing different metrics. If we restrict the space of possible metrics to those of the Robertson-Walker form with a given spatial curvature k, the wave function gives the probability amplitude for observing the Universe in a stat ...
... The wave function of the Universe gives the probability density for observing different metrics. If we restrict the space of possible metrics to those of the Robertson-Walker form with a given spatial curvature k, the wave function gives the probability amplitude for observing the Universe in a stat ...
test 1, April 3, 2009 and solutions
... Test 1 Probability and Statistics I, Friday April 3, 3.30-5.15 A (non-programmed) calculator is allowed, but not necessary. Give short, but motivated answers to the questions. ...
... Test 1 Probability and Statistics I, Friday April 3, 3.30-5.15 A (non-programmed) calculator is allowed, but not necessary. Give short, but motivated answers to the questions. ...
1 - Mathfiles.com
... 3. Finding expected value in roulette. When you give a casino $5 for a bet on the number 7 in roulette, you have a 1/38 probability of winning $175 and a 37/38 probability of losing $5. If you bet $5 that the outcome is an odd number, the probability of winning $5 is 18/38, and the probability of lo ...
... 3. Finding expected value in roulette. When you give a casino $5 for a bet on the number 7 in roulette, you have a 1/38 probability of winning $175 and a 37/38 probability of losing $5. If you bet $5 that the outcome is an odd number, the probability of winning $5 is 18/38, and the probability of lo ...
Probability amplitude
![](https://commons.wikimedia.org/wiki/Special:FilePath/Hydrogen_eigenstate_n5_l2_m1.png?width=300)
In quantum mechanics, a probability amplitude is a complex number used in describing the behaviour of systems. The modulus squared of this quantity represents a probability or probability density.Probability amplitudes provide a relationship between the wave function (or, more generally, of a quantum state vector) of a system and the results of observations of that system, a link first proposed by Max Born. Interpretation of values of a wave function as the probability amplitude is a pillar of the Copenhagen interpretation of quantum mechanics. In fact, the properties of the space of wave functions were being used to make physical predictions (such as emissions from atoms being at certain discrete energies) before any physical interpretation of a particular function was offered. Born was awarded half of the 1954 Nobel Prize in Physics for this understanding (see #References), and the probability thus calculated is sometimes called the ""Born probability"". These probabilistic concepts, namely the probability density and quantum measurements, were vigorously contested at the time by the original physicists working on the theory, such as Schrödinger and Einstein. It is the source of the mysterious consequences and philosophical difficulties in the interpretations of quantum mechanics—topics that continue to be debated even today.