Monday
April 21, 2014

Posts by qwerty


Total # Posts: 202

Probability
Random variables X and Y are distributed according to the joint PDF fX,Y(x,y) = {ax,0,if 1≤x≤2 and 0≤y≤x,otherwise.} 1. Find the constant a. 2. Determine the marginal PDF fY(y). (Your answer can be either numerical or algebraic functions of y). For 0...

Probability
Let X and Y be normal random variables with means 0 and 2, respectively, and variances 1 and 9, respectively. Find the following, using the standard normal table. Express your answers to an accuracy of 4 decimal places. 1. P(X>0.75)= 2. P(X≤−1.25)= 3. Let Z=(Y&#...

Probability
Consider the following joint PMF of the random variables X and Y: pX,Y(x,y)={1/72⋅(x2+y2),if x∈{1,2,4} and y∈{1,3}, 0, otherwise}. 1. P(Y<X)= 2. P(Y=X)= 3. Find the marginal PMF pX(x). pX(1)= pX(2)= pX(3)= pX(4)= 4. Find E[X] and E[XY]. E[X]= E[XY]= 5. var...

Probability
We start with a collection of n (distinguishable) individuals whom we want to split into three possible teams: the blue team, the red team, and the white team. Each individual is randomly assigned to exactly one of the teams according to the following procedure. An individual ...

Probability
To get a complete collection of stamps, Ann needs to have 5 specific (and different) kinds of stamps, denoted by k1,…,k5. She starts out with no stamps. She then receives 5 stamps randomly from a lottery. Each of these 5 stamps has probability 1/5 of being of any particul...

Probability
Alice has five coins in a bag: two coins are normal (i.e., fair with one face Heads and the other face Tails), two are double-headed (i.e., both sides are Heads), and the last one is double-tailed (i.e., both sides are Tails). She reaches into the bag and randomly pulls out a ...

Probability
For each of the following statements, determine whether it is true (meaning, always true) or false (meaning, not always true). Here, we assume all random variables are discrete, and that all expectations are well-defined and finite. Let X and Y be two binomial random variables...

Astronomy
What is the estimated total lifetime for a star with mass 0.7 Msun ? (in billions of year)

Astronomy
The coolest star whose peak blackbody wavelength can be observed with the human eye (the exact range of visible light varies from publication to publication, so use 380nm to 750 nm).

Astronomy
How close to the sun Ganymede would have to be in order to hold water in its atmosphere. (in AU)

Astronomy
A newly discovered planet has a surface temperature of 330 K and a density of 6 g/cm3. What minimum radius does the planet need to have in order to hold water in its atmosphere indefinitely? (in km)

Astronomy
Imagine you are on some far away planetary system looking for planets in the galactic neighborhood and you spot our sun in your sky. In degrees, what is the maximum the orbit can be tilted from 90 in order to see a transiting eclipse (assume the longitude angle is 0)?

Probability
Consider 10 independent tosses of a biased coin with the probability of Heads at each toss equal to p , where 0 < p < 1 . 1. Let A be the event that there are 6 Heads in the first 8 tosses. Let B be the event that the 9th toss results in Heads. Find P(B|A) and express it...

Probability
You are given the set of letters ( A, B, C, D, E ). What is the probability that in a random five-letter string (in which each letter appears exactly once, and with all such strings equally likely) the letters A and B are next to each other?

Probability
The newest invention is a three-sided die. On any roll of this die, the result is 1 with probability 1/2, 2 with probability 1/4, and 3 with probability 1/4. Consider a sequence of six independent rolls of this die. 1. Find the probability that exactly two of the rolls results...

Probability
A group of 90 students is to be split at random into 3 classes of equal size. All partitions are equally likely. Joe and Jane are members of the 90-student group. Find the probability that Joe and Jane end up in the same class.

Probability
A player is randomly dealt a sequence of 13 cards from a standard 52-card deck. All sequences of 13 cards are equally likely. In an equivalent model, the cards are chosen and dealt one at a time. When choosing a card, the dealer is equally likely to pick any of the cards that...

Probability
Alice plays the following game with Bob. First, Alice randomly chooses a set of 4 cards out of a 52-card deck, memorizes them, and places them back into the deck. (Any set of 4 cards is equally likely.) Then, Bob randomly chooses 8 cards out of the same deck. (Any set of 8 ca...

Chemistry
The following questions concern the iconic Nestle Toll House Chocolate Chip Cookie recipe, shown below: 2 1/4 cups all-purpose flour 1 teaspoon baking soda 1 teaspoon salt 1 cup butter or margarine, softened 3/4 cup granulated sugar 3/4 cup packed brown sugar 1 teaspoon vanill...

Chemistry
The following questions concern the iconic Nestle Toll House Chocolate Chip Cookie recipe, shown below: 2 1/4 cups all-purpose flour 1 teaspoon baking soda 1 teaspoon salt 1 cup butter or margarine, softened 3/4 cup granulated sugar 3/4 cup packed brown sugar 1 teaspoon vanill...

Chemistry
1)Buttermilk has 9 grams of protein and 12 grams of carbohydrate per cup (237ml). Estimate the concentration in mol/L of protein using the fact that the average protein is 300 amino acids long and the average amino acid has a mass of 110 amu. 2)Lactose (MW:342 amu) makes up th...

Chemistry
Identify the major macronutrient by weight in each of the following key ingredients. Olive oil Carbohydrates Fats Proteins Buttermilk/milk Carbohydrates Fats Proteins Neither Distilled vinegar Carbohydrates Fats Proteins Plain Greek yogurt Carbohydrates Fats Proteins Which sin...

Chemistry
Which nutrient is most abundant (by weight) in eggplants? Carbohydrates Fats Proteins Add up the total mass of carbohydrates, fats, and proteins in a serving of eggplant. What fraction of the eggplant's weight is made up of these ingredients? Which of the following account...

Astronomy
Basically the ``Bohr radius'' for the dark matter is rB=ℏ^2 / GN M m^2 where m is the dark matter mass, M is the total amount of dark matter mass contained inside the ``gravitational atom'', and ℏ and GN are constants as usual. Taking the dark matt...

Astronomy
How the asymmetry between matter and anti-matter in our Universe might be generated. Why might neutrinos be a key player in achieving this? (a) We already know neutrinos can morph from one neutrino type to another. It is possible, although not certain, that neutrinos could mor...

Astronomy
What percentage of the energy budget do electrons occupy? Take the energy budget occupied by matter to be 4.4%. (a) 3.9% (b) 0.1% (c) 0.03% (d) 0.002%

Astronomy
The Universe is filled with a frozen in Higgs condensate. If this were to suddenly disappear/evaporate, what would happen? (a) All bound matter—nucleons (made of quarks), nuclei (made of nucleons), atoms (made of nuclei and electrons), people (made of atoms), etc.—wo...

Astronomy
What were the relative energy densities in the early Universe? (below, DE means dark energy) (a) They remain roughly equal: rad ∼ mat ∼ DE (b) DE > mat > rad (c) rad > mat > DE (d) mat > rad >...

Astronomy
Which of the below statements about the CMB are true? (i) The “hot” and “cold” spots are areas where photons have slightly more or less energy than average. (ii) It shows that the Universe was accelerating at the time the CMB formed, thus measuring dark ene...

Astronomy
Now imagine you’re an astronomer on Earth looking at the spectrum of an object in space. In the spectrum you are looking for the so-called Lyman- alpha line of hydrogen which occurs at a wavelength of  = 122 nm. In your telescope, you observe the Lyman- ...

Astronomy
How do we image dark matter? (a) We see light from galaxies behind the bullet cluster that is bent (gravitationally lensed) due to the matter (regular and dark) in the bullet cluster. (b) We see light from the gas in the two bullet cluster galaxies and we observe that the gas ...

Astronomy
Where did CMB radiation originate? (a) It is the radiation from the electroweak phase transition when the weak force was spon- taneously broken by the Higgs mechanism. (b) It is radiation from supernovas in the early Universe that produced the heavier elements. (c) The radiati...

Astronomy
Why didn’t the Universe collapse into a black hole in the past when there was so much matter in such a small space? (a) Most of the particles in the early Universe were unstable and decayed before a black hole could form. By the time only stable particles were left (proto...

Astronomy
Each time period corresponds with an event in the list below labeled a to e. Starting with the earliest time period (10^−34 s), list which time period corresponds to which event. For example if you think the times at 10^−34 s, 10^−12 s, 10^−10 s, 3 min,...

Astronomy
Look up where Voyager 1 is now and compute how many lighthours it is away. Round your answer to the nearest number of light hours.

Astronomy
What is the size, i.e. the radius, of a black hole with a mass equal to that of Earth (MEarth=6×1024kg)? Give your answer to one significant figure.

chemistry
A particle with the mass of a proton is trapped in a box. The particle falls from the n=3 state to the n=2 state and emits 0.16 meV of energy. What is the size of the box? Please report your answer in nm.

Quantum Physics
What is the maximum value of the wavelength of light that will ionize the hydrogen atom? Express your answer in units of nanometers.

Quantum Physics
Consider the observable M that corresponds to a measurement in the sign basis where the measurement value is 3 if the outcome is + and -2 if the outcome is - A)Write M in the standard basis. B)If M is the Hamiltonian acting on a qubit which is in the state |phy(0)> = |0>...

Quantum Physics
thanks Andy,Flu and everyone worked for this subject!

Quantum Physics
All wrong?

Quantum Physics
5A: (2/K), (1 - 2/K) 5B: (-2/K), (2/K - 1) 5C: (2/K - 1), (-2/K)

Quantum Physics
Suppose we ran m steps of Grover's algorithm on some function f (which has one marked element y) and the resulting superposition was exactly |y⟩. If we run for m+1 additional steps (i.e. total of 2m+1 steps from the initial state), what is the resulting superpositio...

Quantum Physics
Consider a particle whose wavefunction at some fixed time t is represented by -A if -2≤x≤0 ψ(x)= A if 0≤x≤3 0 otherwise (a) What is the normalization constant A? (b) What is the probability of finding the particle at a position x≤0? (c) What ...

Quantum Physics
Suppose a particle has wavefunction ψ(x,t=0)=Ae^(−x^2/l^2). What is the average value (expectation value) of p, <p>, for this state at t=0?

Quantum Physics
Suppose we have a particle in 1-dimension, with wavefunction Ae^(−|x|/2d). What is the probability to find the particle in the interval [0,d]?

Quantum Physics
The ground state wavefunction for a particle in a shallow potential well in 1 dimension is of the form: Ae^(−|x|/2d). Given that the particle must be found somewhere in the range x∈[−∞,∞], the born rule then places a constraint on the modulus of A...

Biochemistry
Nicotine is a small molecule produced by the tobacco plant Nicotiana tabacum. Nicotine is produced by the plant to discourage herbivores. In low doses, such as those experienced by tobacco users, it is a stimulant that leads to mild euphoria. In high doses, it acts as a potent...

Biochemistry
Amylase is secreted by your pancreas into your small intestine where amylase helps you digest the starches in your diet. Amylase does this because it is an enzyme, a protein that catalyzes a chemical reaction. In this case, amylase catalyzes the breakdown, or hydrolysis, of st...

Genetics
β-thalassemia is a human genetic disease that is inherited in an autosomal recessive manner. Individuals with β-thalassemia produce abnormal hemoglobin which results in a reduced ability to carry oxygen in their blood. The severity of symptoms depends on several gene...

Quantum Physics
Let f:{0,1}->{0,1} with f(101)=1 and f(x)=0 for x ≠ 101 . In this question, we will run through two iterations of the algorithm. (a) What is the superposition after the initialization step? Note that you can describe the superposition Σαx|x> by specifyin...

Quantum Physics
Help please!

Quantum Physics
Help please!

Genetics
Consider the following cross involving the genes for pod color and seed shape: P generation: Green pods with round seeds= ____ Yellow pods with wrinkled seeds=____ F1 generation: 1/4 green pods with round seeds= ____ 1/4 grens pods with wrinkled seeds=____ 1/4 yellow pods with...

Genetics
Remember that the upper-case letter corresponds to the allele with the dominant phenotype. Use the symbols "A" and "a" for pod color and the letters "B" and "b" for seed shape.

Genetics
Mendel also studied pod color, which could be green or yellow, as well as seed shape, which could be round or wrinkled. Consider the following cross: P generation: Yellow pods with round seeds=____ Green pods with wrinkled seeds=____ F1 generation 100% Green pods with round se...

Genetics
Mendel also studied the trait of flower color. Some plants had white flowers, while others had purple flowers. Consider the following cross: P generation: Plant with purple flowers= ____ Plant With purple flowers= ____ F1 generation: 75% plant with purple flowers= ____ 25% pla...

Quantum Physics
a)4;b)4;c)(3,15) or (5,15)

Genetics
In Drosophila melanogaster, the genes for purple eyes (pr) and curved wings (c) are on the same chromosome. The recombination frequency between pr and c is roughly 20%. Both the purple eyed and curly winged phenotypes are recessive to the wild-type (+) phenotypes (red-eyed and...

Quantum Physics
- What is QFT6 of 1/√2(|0> + |3>? - What is QFT6 of 1/√2(|1> + |4>? - What is QFT6 of 1/√3(|0> + |2> + |4>? - What is QFT6 of 1/√3(|1> + |3> + |5>?

Astronomy
Which event is likely to trigger rapid growth in supermassive black hole mass? -A merger of two gas-rich galaxies. -Direct collisions of stellar-mass black holes in collapsing globular clusters. -Tidal disruption of a dwarf elliptical galaxy by a large elliptical galaxy. -A su...

Astronomy
Mergers of two supermassive black holes will be major sources for observations of gravitational waves in the future. What do gravitational detectors aim to detect? -Tiny shifts of fixed objects due to the rippling of space. -Sound waves carried by cosmic ray particles. -Tiny r...

Astronomy
Black holes can be completely described by which three parameters? -angular momentum, spin, and electric charge -angular momentum, density, and radius -mass, angular momentum, and electric charge -mass, angular momentum, and radius

Quantum Physics
Suppose we are given a single qubit which is either in the state |u> = cos(pi/8) |0> + sin(pi/8) |1> or |v> = cos(3pi/8) |0> + sin(3pi/8) |1>. We measure this qubit in the standard basis and guess u if the outcome is 0 and guess v if the outcome is 1. (a) Wha...

Quantum Physics
I) 1/sqrt(2) -1/sqrt(2) 1/sqrt(2) 1/sqrt(2)

Quantum Physics
I) Provide a unitary that maps |+> to |1> and |-> to |0> . Enter 0 in all boxes if no such unitary exists. a b c d II)Provide a unitary that maps |+> to |0> and |-> to |+> . Enter 0 in all boxes if no such unitary exists. a b c d III)Provide a unitary t...

Quantum Physics
Let |ψ> = a|0>+b|1> where a and b are nonnegative real numbers. We know that if we apply H to this qubit and then measure the resulting state in the sign basis, the probability of getting a + is 1/4 (a) What is |ψ> in the standard basis? |0> = |1> =...

Astronomy
What causes the ionization of the Intergalactic Medium (IGM)? - radiation from star-forming galaxies and quasars - residual radiation from inflation - heat generated from combustion in the IGM - the baryon density of the IGM

Astronomy
At what cosmic time was/is star formation density at its peak? -At present time. -Within the first billion years after the Big Bang. -At about few billion years after the Big Bang. -About few billion years ago.

Astronomy
Which of the following can be considered evidence of galaxy evolution observed in the Milky Way? - differential rotation of the galactic disk - existence of different populations of stars - existence of hot gas in the interstellar medium - the rotational velocity curve

Biology
Dopamine is a neurotransmitter—a chemical released by nerve cells to send signals to other nerve cells. Activities like sex and gambling increase the levels of dopamine released within the brain. The highly addictive drugs cocaine and methamphetamine mimic the effects of...

Biology
Which of the following bond types is Testosterone capable of forming with a suitable partner molecule? Indicate your answer by checking "Yes" or "No" as appropriate. Hydrogen Bond Ionic Bond van der Waals forces As a whole, is the Testosterone molecule: - H...

Chemistry
Given the part of the molecule shown below, can the red atom participate in a hydrogen bond with an approriate bonding partner? -O-H -C-H -N-H -O-H -C-H -N-H

Chemistry
Given these pairs of atoms, indicate whether the following bonds are polar or non-polar covalent bonds. C-H N-H O-H C-C

Chemistry
For each of the following, enter the number of covalent bonds that the atom can form: (A) One atom of carbon (B) One atom of sulfur (C) One atom of nitrogen with no net charge (D) One atom of nitrogen with positive net charge (E) One atom of oxygen with no net charge (F) One a...

Chemistry
An equilibrium mixture contains 0.250 mol of each of the products (carbon dioxide and hydrogen gas) and 0.200 mol of each of the reactants (carbon monoxide and water vapor) in a 1.00-L container. CO(g) + H2O(g) <-> CO2(g)+ H2(g) How many moles of carbon dioxide would hav...

Quantum Physics
Suppose Alice starts with two qubits in the Bell state 1/√2 (|00> + |11>) and teleports these qubits to Bob by applying the quantum teleportation protocol to each qubit separately. (a) What is the state of the two qubits received by Bob? |00> = |01> = |10>...

Quantum Physics
Suppose H|ψ> = 1/√2 (|000> + |111>). What is |ψ> ? Specify the probability amplitude for each component: |000> = |001> = |010> = |011> = |100> = |101> = |110> = |111> =

Astronomy
Which type of emission closely traces the star-forming regions of a galaxy? - molecular CO emission - coronal X-ray emission - 21 cm emission - none of these

Astronomy
The majory of galaxies (by number) are: - barred spirals - giant ellipticals - lenticulars - dwarfs

Quantum Physics
Alice and Bob share a state a|++> + b|-->, where the first qubit is Alice's and the second qubit is Bob's. Alice measures her qubit in the standard basis and sends the measurement outcome to Bob. If Bob wants his qubit in a|+> + b|->, what gate does he appl...

Quantum Physics
What is ZX applied to H|0>?

Quantum Physics
Suppose we have a qubit in the state |ψ>. We know that if we measure it in the standard basis, the probability of getting a 0 is 7/9. Now, if we instead first apply a Hadamard gate and then measure the resulting qubit H|ψ> in the sign basis, what is the probabi...

Quantum Physics
Suppose we have two qubits in the state α|00⟩+β|11⟩. (a) If we measure the fi rst qubit in the sign basis, what is the probability of seeing a +? (b) What is the resulting state of the second qubit in that case?

Quantum Physics
Suppose that a qubit is in the state |ψ> = a |0> + √ (1-a^2)|1> where a [-1,1] . If we first perform a standard basis measurement on this qubit and then perform a |u>, |u⊥> -basis measurement where |u> = b |0> + √ (1-b^2)|1> for s...

Physics
9/14

Physics
a=1/2

Physics
sqrt(2)/3 |00> + 1/3 |01> + 2/3 |10> + sqrt(2)/3 |11>

Physics
(1+sqrt(2))/sqrt(6)|+> + (1-sqrt(2))/sqrt(6)|->

Physics
(1+sqrt(2))/sqrt(6)

physics
(a) 0.5 (b) 67.5 (c) 0.7285

physics
Problem 10: 3/4 Problem 11: a=3/5, b=8/10

Quantum Physics
We have a qubit in the state |ψ>= √3/2 |0>+ 1/2 |1>, which we want to measure in the {Cos θ |0> + Sin θ |1>, Sin θ |0> - Cos θ |1>} basis. In order for the two possible outcomes to be equiprobable, what should be the value of...

Cosmology
A curvature constant of k=0, as used in the Friedmann equation, means: * The universe is open * The universe is matter-dominated * There is no dark energy * The universe is flat

Cosmology
In an Einstein-de Sitter (matter-dominated) universe, the scale factor is proportional to time to the power of: * 3/2 * 2/3 * 1/2 * -1/3

Cosmology
In order from earlier to later times, the dominant components of our universe have been: * dark energy, matter, then radiation * dark energy, radiation, then matter * matter, radiation, then dark energy * radiation, matter, then dark energy

Cosmology
In a universe where the scale factor is proportional to t^α, where t is time and α is a constant less than one, the universe has: * the sign of the acceleration is undetermined * negative acceleration * positive acceleration * zero acceleration

Cosmology
Lookback time for a given redshift, tL(z), is... * time between the given redshift and the beginning of the Universe. * time between the infinite and the given redshift. * equal to the age of the Universe at the given redshift. * time between now and the given redshift.

Cosmology
As compared to Cepheids, RR Lyrae stars are... * fainter and slower pulsating. * brighter and faster pulsating. * fainter and faster pulsating. * brighter and slower pulsating.

Cosmology
In the Tully-Fisher relation, the scatter is minimized at which wavelength? * Red * Blue * Infrared * UV

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