4. Probability

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 $\mathrm{statistic}$?

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?

Which term best describes the process of using numbers and graphs to understand and interpret information about our world?

Given the exponential probability density function $f\left(x\right)=\lambda e^{-\lambda x}$ for $x\ge 0$ and $\lambda >0$, what is the expected value (mean) of $X$?

If $30$ is what percent of $120$? Identify the percent, amount, and base in this problem.

Which of the following is a reason that $\mathrm{Six} \mathrm{Sigma}$ methodologies rely heavily on data analysis?

Which of the following correctly states the two requirements for a discrete probability distribution?

Given the following table, does it represent a valid discrete probability distribution? x: $1$ $2$ $3$ $4$ P(x): $0.2$ $0.3$ $0.4$ $0.1$