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

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