The sampling distribution of frac{S_{1}^{2}}{S_{2}^{2}} is the chi^2 distribution. Give a correct answer true or false inference for two population variances is done through their difference.

Solve the following problems applying Polya’s Four-Step Problem-Solving strategy.
If six people greet each other at a meeting by shaking hands with one another, how many handshakes take place?

In how many ways can 7 graduate students be assigned to 1 triple and 2 double hotel rooms during a conference

A privately owned liquor store operates both a drive-n facility and a walk-in facility. On a randomly selected day, let X and Y, respectively, be the proportions of the time that the drive-in and walk-in facilities are in use, and suppose that the joint density function of these variables is
$f(x,y)=\{\begin{array}{ll}\frac{2}{3}(x+2y)& 0\le x\le 1,0\le y\le 1\\ 0& ,elsewhere\end{array}$
a) Find the marginal density of X.
b) Find the marginal density of Y.
c) Find the probability that the drive-in facility is busy less than one-half of the time.

Christine's test scores are 89, 94, 88, 75, and 94. What does Christine need to score on the next test to have a median score of 90?

A colleague of yours is completing a final report on the causes of the frequency of cyberbullying. In this report, she is asked to identify the causes that most strongly impacted the frequency of cyberbullying. She conducts an OLS regression.
What statistic do you advise her to use in her discussion? Why?

statement of the proof was that $S$ was closed from below, and bounded from below. It is fine when they say that $B$ is bounded below which is also obvious from the definition. So, there should be a g.l.b. for the set $B$, which is denoted by $b_0$.
Now why there should exist a sequence of points $\left({\mathbf{y}}^{\mathbf{(}\mathbf{n}\mathbf{)}}\right)$ in the risk set $S$ such that $\sum p_j{y}_j\to b_0$? Is $b_0$ a limit point of $B$? Is $B$ closed ? Even if this happen why $b_0$ which is greatest lower bound of $B$ should belong to $B$?
Next, I guess they apply Bolzano Weierstrass theorem to say that ${\mathbf{y}}^{\mathbf{0}}$ is a limit point of the sequence $\left({\mathbf{y}}^{\mathbf{(}\mathbf{n}\mathbf{)}}\right)$. But why the last step $\sum p_j{y}_j^0=b_0$?

Find the correlatin coefficient r using bivariate data.