Question: 2015 Fall Final - 17

Author: Michiel Smid

You are given that:

The course COMP 9999 runs over a period of one year, starting on January 1 and ending on December 31. There is one lecture every day; thus, the total number of lectures is 365.
At the beginning of each of the 365 lectures, Nick flips a fair and independent coin twice. If the coin comes up heads twice, then Nick eats 3 bananas during the lecture; otherwise, Nick eats 5 bananas during the lecture.

Let $X$ be the total number of bananas that Nick eats during the 365 lectures of the course COMP 9999. What is the expected value $\mathbb{E}(X)$ of $X$?
(n.b., you may find it useful to apply Linearity of Expectation)

(a)

$\frac{7 \cdot 365}{2}$

(b)

$\frac{9 \cdot 365}{2}$

(c)

$\frac{5 \cdot 365}{2}$

(d)

$4 \cdot 365$