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Consider a DMS with a two-symbol alphabet source with n = 100 000.
f) Find the mean and variance of Na. Approximate by the central limit theorem approximation. The central limit theorem approximation is to evaluate assuming that Na is Gaussian with the mean and variance of the actual Na.One point of this exercise is to illustrate that the Chebyshev inequality used in bounding PrT in the text is very weak (although it is a strict bound, whereas the Gaussian approximation here is relatively accurate but not a bound). Another point is to show that n must be very large for the typical set to look typical.
Footings for a structure are to be built beneath a basement slab on a clay at a depth of 20 ft. below present ground level. Representative consolidation tests on the soil produce a 0.043 slope of recompression curve. The groundwater table is 15 ft. b..
A well-insulated rigid vessel of volume 0.2 m^3 is divided into two equal compartments by thin diaphragm, as illustrated in the accompanying figure. One of the compartments is a vacuum
Calculate the magnitude and show the location of the maximum compressive and tensile normal stresses on the cross-section and calculate the maximum magnitude of the internal bending moment
A 6-lane freeway horiz. alignment has a 1200’ C.L. radius going into a tangent and then a reversing 1800’ radius. How much tangent distance between the two curves is needed to meet the superelevation runoff requirements?
Flange thickness hf= 0.2h and web width bw=0.4. The member will be prestress using graded 270 strand. Time dependant losses are estimate at 20% of Pi. Normal density concrete will be used with f'c = 5000 psi
Consider a 2014-T6 aluminum alloy the S-N behavior. A cylindrical rod of diameter 13.2 mm fabricated from this alloy is subjected to repeated tension-compression loading along its axis. Compute
A submerged stratum of clay has a thickness of 15m. The average water content of samples taken from the stratum is 54%, and the specific gravity of the solid constituents is 2.78.
Describe the use of productivity models for estimating land productivity. Provide details about various attributes that can be used and how the model is developed . Examples can be used to demonstrate model workability.
Determine the maximum and minimum stress intensities in the section.
A trapezoidal channel cut into rock has a bottom width of 4 ft, side slopes of 1:1 and a channel slope of 0.0005. What is the critical slope of the channel.
Find the percentage of Air voids and voids in the mineral aggregate if the asphalt absorption is .5%, and the specific gravities of the aggregate and binder are 2.660 and 1.020 respectively. The unit weight of the mixture is 2.39 Mg/m^3
vehicles begin to arrive at a toll booth at 850 am with an arrival rate of xt 4.1 .01t with t in min and xt in veh
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