7. An image with intensities in the range [0, 1] has the PDF pr(r) shown in the following diagram. It is desired to transform the intensity levels of this image so that they will have the specified PDF pz(z) shown. Assume continuous quantities and find the transformation in terms of r and z that will accomplish this. P,(r) P:(z) 2

2. Consider the following two functions: z = f(x, y) = (x – 2y), z = g(x, y) = (r – 2y)?. (a) Give the level curves for both f and g consisting of the (z = 0,1, 2, 3)-values. Label each level curve with the respective z value. (b) Let S be the graph of f and let T be the graph of g. Turn your two level curve diagrams in part (a) into separate sketches of S and T in three-dimensional coordinate system by plotting the level curves at the appropriate altitude. (c) Both S and T are examples of one of our familiar named surfaces. Use their defining equations and your sketches in part (b) to identify which.