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1. State the optimal properties of maximum likelihood estimators (finite sample and asymptotic).
2. Explain the difference between:
(a) Fisher's sample and individual observation information,
(b) Fisher's information and observational information matrix,
(c) Fisher's information and conditional information matrix.
A classical particle of mass m moves in 1 dimension and is attached to an ideal spring of spring constant mw_0^2 . Ignore friction. Take the equilibrium position of the particle to be the origin of the particle’s position x.
A 639keV x-ray photon scatters from an electron at rest, deflecting through 105°. What is the scattered photon's energy
The maximum torque experienced by a coil in a 0.80 T magnetic field is 8.4 10-4 N · m. What is the length of the wire from which the coil is made
the ocean of the world covers three-quarters of the earths surface and have an average depth of 3.8 km. if the
When a 2.10-kg object is hungvertically on a certain light spring described by Hooke's law, the spring stretches 2.84 cm. What is the force constant of the spring?
The tension at which a fishing line snaps is commonly called the line's "strength." Find what minimum strength is needed for a line that is to stop a salmon of weight 85 Newton in 8.9 centimeter
A cube of ice is taken from the freezer at -8.7°C and placed in a 97 g aluminium calorimeter filled with 351 g of water at the room temperature of 20°C. The final situation is observed to be all water at 19°C. What was the mass of an ice cube.
A proton is confined to a nucleus that has a diameter of 5.7 10-15 m. what is the minimum uncertainty in its momentum
Two canoes are tied together and traveling down a river with the current. Spotting a waterfall, the two canoeists cut the rope, What is the combined mass of this canoe and rider
Consider a vibrating piano string. The string is under a tension T, has a length L and diameter d. What is the frequency f' for the second string
A bat at rest sends out ultrasonic sound waves at 48 kHz and receives them returned from an object moving directly away from it at 27.5 m/s. Determine what is the received sound frequency
A convex mirror has a focal length of -33.0 cm. A 14.0-cm-tall object is located 33.0 cm in front of this mirror. Determine the (a) location and (b) size of the image.
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