A quarterback throws a football at a target marked out on the ground 40 yards from his position. Assume that the PDF for the football’s hitting the target is Gaussian within the plane of the target. Let the coordinates of the plane of the target be denoted by the x and y axes. Thus, the joint PDF of (X, Y) is a two- dimensional Gaussian PDF. The average location of the hits is at the origin of the target, and the standard deviation in each direction is the same and is denoted as σ. Assuming X and Y are independent, find the probability that the hits will be located within an annular ring of width dr located a distance r from the origin; that is, find the probability density function for hits as a function of the radius from the origin.
Answer to relevant QuestionsLet and be independent and both exponentially distributed with Find the PDF of Z = X –Y. Suppose is a Rayleigh random variable and is an arcsine random variable, so that Furthermore, assume X and Y are independent. Find the PDF of Z = XY. For positive constants and, a pair of random variables has a joint PDF specified by . Fx, y (x, y) = abe-(ax = by) u (x) u (y) (a) Find the joint CDF, Fx, y (x, y). (b) Find the marginal PDFs, fx (x) and fy (y). (c) Find ...Repeat Exercise 5.66 Suppose In figure 5.7 and P i = 1/3, i = 1, 2, 3. Determine the mutual information for this channel. If A pair of random variables has a joint PDF specified by fX, Y( x, y) = d exp (–( ax2+ bxy+ cy2)) (a) Find the constant in terms of a, b, and c. Also, find any restrictions needed for a, b, and c themselves for this to be a ...
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