Problem 5 The hourly volume of traffic X for a proposed highway is distributed as in the figure below. (a) Determine and plot the CDF of X, FX (x) . (b) The traffic engineer may design the highway capacity equal to the following: (i) The mode of X. (ii) The mean of X. (iii) The median of X. (iv) The mean plus one standard deviation of X. (v) x.90, the 90-percentile value, which is defined as F (x 90 ) = 0.90. Determine the design capacity of the highway and the corresponding probability of exceedance (that is, capacity is less than traffic volume) for each of the four cases.(c) Assume that the actual capacity of the highway after it is built is either 300 or 350 vehicles per hour with relative likelihoods of 1 to 4. Plot the PMF of the capacity of the freeway. What is the probability that the capacity will be exceeded? (d) Follow up on part (c): It is known that the capacity of the freeway has been exceeded. Update the PMF of the capacity of the freeway in light of this information. fx(x) 0 100 200 300 400 x. number of vehicles per hour