4. Probability

In a three-server queueing model where arrivals follow a Poisson process with rate $\lambda$ and service times are exponentially distributed with rate $\mu$ per server, what is the probability that there is exactly $1$ customer in the system at steady state?

Which of the following is an example of inferential statistics?

The accuracy of a poll is limited by its $\mathrm{\_\_\_\_\_}$.

If $11$ out of $20$ students in a class passed an exam, what is the probability that a randomly selected student from this class passed the exam? Express your answer as a simplified fraction.

Which of the following examples best represents a simple random sample?

Which of the following best describes a confounding variable in the context of probability and statistics?

In the context of basic probability and statistics, which type of monitoring methodology is designed to detect statistical deviations from a baseline?

Which of the following statements is true about the independence of events $a$ and $b$?

Which of the following is a property of the $S\text{'}t$-distribution?

Which characteristic must be known about a data set before the empirical rule can be applied?

Which of the following is a qualitative forecasting method?

Suppose the probability density function is given by $f\left(x\right)=\frac{1}{2}$ for $0\le x\le 2$ and $f\left(x\right)=0$ otherwise. What is the probability that $x$ is between $1$ and $3$?

In the context of probability, what is the sample space when rolling a standard $6$-sided die?

Which characteristic must be known about a data set before the empirical rule can be applied?