4. Probability

In the context of regression analysis, which of the following best describes the requirements for independent and dependent variables?

Why is it important to be skeptical of statistical results reported in the media?

Which of the following best describes the probability of an event A, denoted as $P\left(A\right)$?

Sampling error best fits which of the following descriptions?

If the probability of an event is $p=0.6$, what is the probability that the event does not occur?

In statistics, why is a $\mathrm{sample}$ used more often than a $\mathrm{population}$ when conducting $\mathrm{probability}$ studies?

Let the random variables $X$ and $Y$ have joint pdf $f(x,y)=2$ for $0<x<1$, $0<y<x$, and $f(x,y)=0$ otherwise. Find $P(Y<0.5,X>0.5)$ (round off to third decimal place).

Which of the following is a requirement for a probability distribution?

In probability theory, when is it appropriate to calculate the $\mathrm{expected value}$ of a random variable?

Which of the following is an example of a continuous random variable?

In a study, the mean height of all students in a university is calculated using the heights of every student. Is this mean value a $\mathrm{parameter}$ or a $\mathrm{statistic}$?

Text Twist

In the game Text Twist, six letters are given and the player must form words of different lengths using those letters. Suppose the letters in a particular game are ENHSIC.

c. The solution to this game has three 6-letter words. To move to the next round, the player must get at least one of the six-letter words. If the player simply guesses, what is the probability of getting one of the six-letter words on the first try?

In the context of probability, which of the following best describes the difference between a $\mathrm{marginal}$ distribution and a $\mathrm{conditional}$ distribution?

In the context of probability, what does it mean when sampling is done without replacement?

Which of the following terms best describes a process of analyzing data to identify meaningful relations?