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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+bYWhere 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.
A 2.50-g sample of a large biomolecule was dissolved in 13.0 g of carbon tetrachloride. The boiling point of this solution was determined to be 77.85°C. Calculate the molar mass of the biomolecule.
determine the force in members GF,FB, and BC of the Fink truss and state if the members are in tension or compression
The wastewater treatment plant for Pine City discharges 1 × 105 m3/day of treated waste to the Pine River. Immediately upstream of the treatment plant, the Pine River has an ultimate CBOD of 2 mg/L and a flow of 9 × 105 m3/day.
A reverse osmosis plant desalinates 5X10^6 L/day of feedwater containing 1500 mg/L of salts, yielding 3X10^6 L/day of product water with 75 mg?l of salt. What would the salt concentration be in the brine?
Vehicular access to the Toronto Island Airport now involves the use of a small ferry, capable of carrying about 8 automobiles or an equivalent number of trucks, which operates across the 150 metre wide body of water known as the Western Gap
A 3000-lb car is traveling on a paved road with Cd (coefficient of drag) = 0.35, Af (frontal area of the vehicle) = 21ft^2, and p(air density)=0.002378 slugs/ft^3. Its engine is running at 3000rpm and is producing 250ft-lb of torque.
To float a 160 pound man using helium balloons (assume 0.52 cubic feet per inflated balloon). How many balloons would it take? Assume density of air is 1.29 kg/cubic meter and the density of helium is 0.179 kg/cubic meter.
A concrete dam retaining water has a specific weight of concrete of 23.5kn/m3, what is the factor of safety against sliding & overturning and pressure intensity on the base if coefficient of friction is 0.45
For a flow of 2 MGD, an influent BOD of 200 mg/l, a depth of 8 feet, and a desired effluent BOD concentration of 20 mg/l, determine the volume required for trickling filtration treatment as predicted for single-stage treatment by using NRC equatio..
A pig farmer owns a 20-arce farm and started business with 22.1 pigs. After one year, he has 319 pigs. Assuming a constant growth rate, what is the doubling time in units of days.
if the settling velocity of a particle is 2.80 mm/s and the overflow rate of an up flow clarifier is 0.560 cm/s, what percent of the particles are retained in the clarifier. If the flow rate of this problem is doubled
A hollow circular, gray cast-iron pipe supports a red brass rod and weight W = 2 kips, as shown. The outside diameter of the pipe is d = 6". If the allowable compressive stress in the pipe is 5000 psi and the allowable shortening of the pipe is 0...
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