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Discuss how the effectiveness of Skilling's method scales with dimensionality, using a correlated N-dimensional Gaussian distribution as an example. Find an expression for the rejection probability, assuming the Markov chain is at equilibrium. Also discuss how it scales with the strength of correlation among the Gaussian variables. [Hint: Skilling's method is invariant under affine transformations, so the rejection probability at equilibrium can be found by looking at the case of a separable Gaussian.]
Our sun has a surface temperature of 6000oK. The star Antares has a surface temperature of 3400oK and a diameter 300 times greater than our Sun. Find to which group of stars does Antares belong, and why
The current in an RL circuit builds up to one-third of its steady state value in 3.80 s. Find the inductive time constant
If the partial pressure of water vapor is 47 mm Hg in the lungs at 760 mm Hg pressure, what percentage of air does the water vapor constitute?
A 250 g, 40.0-cm-diameter turntable rotates onfrictionless bearings at 61.0 rpm. A 17.0 g block sits at the center of the turntable. What is the turntable's rotation angular velocity when the blockreaches the outer edge
A piano string having a mass per unit length equal to 4.00 × 10-3 kg/m is under a tension of 1100 N. Find the speed with which a wave travels on this string.
it is found experimentally that the electric field in a certain region of earths atmosphere is directed vertically
What is the total force (magnitude and direction) exerted by these two charges on a third charge q3=+5.00 nC located at y=-0.4000m
There are two light bulbs in a circuit, powered by one battery. One light bulb is a 100 watt light bulb and the other a 200 watt light bulb. How much power must the battery be supplying for the lights to be running at full power?
An elephant has legs that stretch 2.3 from its shoulders to the ground. How much time is required for one leg to swing forward after completing a stride, how many steps per minute will the elephant take
A projectile is fired upward at an angle of 45.0o from the top of a 165 meter cliff with a speed of 175 m/s. Determine what will be its speed when it strikes the ground below
An electron is given a velocity v_0 and is projected along an axis midway among the CRT deflection plates where there exists an E-field directed upward. Ignoring any effects due to gravity, decide the magnitude and direction of the electron's acceler..
The plates of a spherical capacitor have radii 33.0 and 42.0 mm. Calculate the capacitance. What must be the plate area of a parallel-plate capacitor withthe same plate separation and capacitance?
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