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A joint ensemble XY has the following joint distribution.
What is the joint entropy H(X, Y )? What are the marginal entropies H(X) and H(Y )? For each value of y, what is the conditional entropy H(X | y)? What is the conditional entropy H(X | Y )? What is the conditional entropy of Y given X? What is the mutual information between X and Y ?
Give four reasons why Lavoisier is generally designated "the father of chemistry." When a sample of A reacts with one of B, a new substance AB is formed, and no B but a little of A is left. Which is the limiting reactant?
A subatomic particle has an unknown lifetime τ. The particle is created at t = 0 and travels around the Earth's equator at speed 0.9896c. If the particle decays at the moment it completes one trip around the Earth, what is?
A violinist is tuning her instrument to concert A (440 Hz ). She plays the note while listening to an electronically generated tone of exactly that frequency, What was the frequency of her violin when she heard the 4.00 beat
The wind exerts on a flower the force 0.755 N horizontally to the east. Find the vector torque of the wind force about the base of the stem
The Ed-Scale defines the perfect temperature of a martini to be 14 degrees E and the boiling point of antifreeze to be 100 degrees E. Use this equation to find the freezing point of water in Eds
In a material having an index of refraction n , a light ray has frequency f, wavelength ?, and speed v. What is the frequency of this light in vacuum and in a material having refractive index n1
A cube of ice is taken from the freezer at -8.7^circ C and placed in a 114 g aluminium calorimeter filled with 329 g of water at room temperature of 20.0 ^circ {rm C}. The final situation is observed to be all water at 15.0^circ C.
An astronaut who is repairing the outside of her spaceship accidentally pushes away a 96.7-cm-long steel rod, What is the magnitude of the EMF, in millivolts, induced between the ends of the rod
A heavy-duty stapling gun uses a 0.131-kg metal rod that rams against the staple to eject it. The rod is pushed by a stiff spring called a "ram spring" (k = 31800 N/m).
Unpolarized light passes through two polarizers in turn withpolarization axes at 45° to each other. What is the fraction ofthe incident light intensity that is transmitted?
A brave child decides to grab on to an already spinning merry-go-round. What is the moment of inertia of the merry-go-round with respect to its central axis
a cameras zoom lens covers the focal-length range 38mm -138mm. you point the camera at a distant object and photograph
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