please work one the following:

• 5 & 6
• 8

n 1. Let ((x : M, o) = In ( 20 k - 16 ) 2 1 V2702 exp 202 Treating the values of a = [x1, 2, ..., In] as constants, at what value of u, o does ((@ : M, ) have a maximum? You only need to find the single critical number (and argue that it is the only one) to receive full credit. Extra credit may be given for fully justifying that this is in fact a maximum. 2. Convert the point at r = 7, 0 = 27/3 to rectangular coordinates. 3. Evaluate over the region R = [0, 1] x [0, 2]. Be wise about which order of integration you choose. 4. For each of the following, sketch the region of integration and change the order of integration. (a ) JI. s( ,y ) dy da 5. Suppose that the function f(x, y) defined below is a probability density function: f (x, y) = if (x, y) E [0, 1] x [0, 1] and y S x otherwise Find the value of c. 6. For the probability density function given in the previous problem, find the probability that the pair (x, y) satisfies y ~ zx. 7. A uniform probability density function is defined on the region [0, 2] x [0, 1]. Find the probability that the pair (x, y) satisfies y