Question

Suppose Johnny allows himself to eat a box of candy a day (he’s on a diet). He wakes up at 10am and finishes the box before 2pm [0,4]. Suppose that the completion time in hours, T, for the time to eat the box follows the density: f(t) = c(4t − t 2 ), 0 ≤ t ≤ 4

(a) (3 points) find the constant c.

(b) (2 points) What is the probability that Johnny will finish his box of candy before the 1st hour?

(c) (2 points) What is the median time it takes Johnny to finish the candy?

(d) (2 points) What is Var(3T)

Answer 1