4. Most people don't last long on diets. In fact, you can model how long a person will last before c - aft/4, t 2 0 . . 0 lse be the pdf of a continuous random variable for the , e time in days until a random person quits a diet. giving up on a diet. Let q(t) = { a. Find the particular number c must be if q(t) is to be a valid pdf. (You'll need this value below.) b. Find the probability a random person lasts exactly 6.283185 days before quitting. c. Find the probability a random person lasts at least a week before quitting. d. A clickbaity e-mag is looking for a quote of the form \"90% of all dieters quit within 9: weeks!\". Find as. (a: need not be an integer.) e. On average, how long does a person last on a diet? (Carefully show every step! This will take a good deal of work, which should not be skipped, even if you know some quick approach.)