Problem 2. (50 points) a. If maximum willingness to pay for movie tickets is uniformly distributed between $5 and $15 with w(x) = 1/10, and the maximum weekly demand at a movie theater is 5000, estimate the demand function for this theater. (10 points) b. Plot the maximum willingness to pay distribution function and demand function. (10 points) c. If the maximum willingness is a linear function w (x) = 100 x estimate the demand function. (10 points) d. Plot the maximum willingness to pay distribution function and demand function. (10 points) Note: 5 axdx = {ax? e. If demand function for this theater is d = 10000 - 500p, what is the distribution function of maximum willingness to pay? (10 points) Note: The slope of the demand function at any price point is the density function of maximum willingness to pay at that price. To get the slope, assumed is dependent variable y, and p is independent variable X