PROBLEM 1 (35pts) [See book Problem 5-55 on p.183] In an acid-base titration, a base or acid is gradually added to the other until they have completely neutralized each other. Let X and Y denote (the act of measuring) the milliliters of acid and base, respsectively, needed for equivalence. Assume that .

(a)(5pts) For find .

Solution:

(b)(5pts) Find .

Solution:

(c)(10pts) Find .

Solution:

(d)(5pts) Find . To this end, write a Matlab code that uses the Matlab command mvncdf. Include your code HERE.

Solution:

(e)(10pts) Find . To this end, (i) show the event as a shaded area in an x-y plot. Then (ii) write a Matlab code that uses the Matlab command mvncdf. Include your code HERE.

Solution:

Figure 1(e) Plot showing the event.