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A surveyor measures an angle with two instruments; call them A and B. Both instruments produced unbiased measurements, but the standard deviation of measurements made with instrument A is twice that of B. Due to environmental effects (wind, thermal expansion, etc) simultaneous measurements made with the two instruments have a correlation of r=0.5.
Let X and Y be random variables representing simultaneous measurements of a bearing made with instruments A and B, respectively. You are going to use a linear combination of the two measurements as your estimator (call it S) of the true bearing (call it s):
S=aX+bY
Where a and b are predetermined weights.
(a)What conditions must be placed on the weights a and b so that E[S]=s
That is, so that S is an unbiased estimator of s?
(b)What values of a and b will minimize the variance of S? The answer to this question will take the from a equals a specific number and b equals a specific number.
At Point A in a pipeline carrying water (? = 62.4 lb/ft3) the diameter is 3.0 ft, the pressure is 11 psi, and the velocity 4 ft/s. At Point B, 6 ft higher than Point A, the diameter is 2.5 ft and the pressure is 4 psi
Estimate C and of the rock mass and estimate the uniaxial compressive and tensile strengths of the rock mass
Ship A leaves port sailing in a direction 60 degree C north of due east and sails for 12 hours at 10 knot . Sheep B leaves the same port 3 hours later and sails due east at 25 knot for 9 hours. How far apart (in nautical miles) are they at this time?..
HJ Heinz Corporation is constructing a distribution facilityin Italy for products such as Heinz Ketchup, Jack Daniel's Sauces,HP steak sauce, and Lea & Perrins Worcestershire sauce. A15-year life is expected for the structure.
Account for chemical reactions, groundwater flows, streams, precipitation, evapotranspiration. Indicate any assumptions that can be made to simplify your equation.
The initial concentration of carbon in the metal is 0.1wt%. We first do an experiment by applying a concentration of 5%wt of carbon at the surface of a similar slab and maintaining the system at 900 K for an hour.
A large parabolic antenna is designed against wind load. During a wind storm, the maximum wind-induced pressure on the antenna, P, is computed as P= 1/2CRV^2 Where C = drag coefficient, R = air mass density in slugs/ft3, V = maximum wind speed in ft/..
Determine the height of capillary rise of benzene in a clean glass tube of 0.01 inches ID at a temperature of 20 degrees Celsius. Assume λ = 65 degrees Celsius.
A dense sand has an effective friction angle of 43 and c'=0. A dry, 2.8-inch diameter sample is tested in drained triaxial shear with a confining pressure of 2500 psf. What axial load, P (in pounds), will be required to fail the sample?
What is the step by step when design a reinforce concrete (t-beam and rectangular beam), slab doubly reinforce?
If a tractor with 23-hp, a max speed of 3.6 mph in 1st gear and an effieiciency of 92% is operated operated down a 4% slope and the rolling resistance is 80 lb/ton, what is the maximum external pull in each of the 4 gears.
What is the normality of a sodium hydroxide solution that contains 250 mg/L NaOH in 2.3 L solution? What is the concentration in mole/L and mg/L as CaCO3. Na = 23, OH = 17
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