$\IFeelLikeSinging(n):$
$\quad \mathbf{if}\ n = 0\ \mathrm{or}\ n = 1\ \mathbf{then}$
$\quad \quad \text{sing O Canada}$
$\quad \mathbf{else}\ \mathbf{if}\ n\ \text{is odd}\ \mathbf{then}$
$\quad \quad \IFeelLikeSinging(n + 1)$
$\quad \mathbf{else}$
$\quad \quad \IFeelLikeSinging(\frac{n}{2})$
$\quad \quad \IFeelLikeSinging(\frac{n}{2} - 1)$
When Nika writes the exam, what is the expected number of questions that appear on the exam and that Nika has practiced on?
(n.b., depending on your background, it may be helpful to observe that this can be modelled using the hypergeometric distribution)What is the expected value $\mathbb{E}(X)$ of the random variable $X$?
Hint: Use indicator random variables.Experiment: Roll each die once and take the sum of the two rolls. You repeat this experiment until the sum of the two rolls is equal to 7. Consider the random variable
For any random variable $X$, $\mathbb{E}\left(1 \middle/ X \right) = 1 / \mathbb{E}(X)$.
(i) | $k$ of these $n$ students are politically correct and, thus, refuse to say Merry Christmas. Instead, they say Happy Holidays. |
(ii) | $n - k$ of these $n$ students do not care about political correctness and, thus, they say Merry Christmas. |
Define the random variable $X$ as the number of positions $i$ with $1 \leq i \leq \left. n \middle/2 \right.$ such that both students at positions $i$ and $2i$ are politically correct.
What is the expected value $\mathbb{E}(X)$ of the random variable $X$?Hint: Use indicator random variables.