Second Examination Study Guide

You can also download a PDF copy of this study guide.

1. Understand what is meant by random variables, and discrete versus continuous quantitative random variables.

2. Understand what is meant by the probability distribution of a discrete random variable.

3. Understand what is meant by a population distribution and a sampling distribution.

4. Be able to compute the mean, variance, and standard deviation of a discrete random variable from its probability distribution (when given as a table of values and probabilities).

5. Know how to compute probabilities using the probability distribution of a discrete random variable.

6. Know how to compute probabilities using the probability distribution of a continuous random variable.

7. Know how to compute probabilities using a normal probability distribution (with statdistributions.com).

8. Know how to derive a sampling distribution using the five-step method.

9. Know how to use the binomial distribution to derive the sampling distribution of $\hat{p}$.

10. Know how to find/compute the mean and standard deviation of $\bar{x}$ and $\hat{p}$.

11. Know how to find the interval that has a probability of approximately 0.95 of containing $\bar{x}$ or $\hat{p}$.

12. Understand what it means to say that a statistic is unbiased.

13. Understand what is meant by the standard error of a statistic.

14. Understand what is implied by the central limit theorem.

15. Why do we divide by $n-1$ rather than $n$ when computing $s^2$?

16. Be sure you know the notation (i.e., symbols) we have used (e.g., $\mu$, $\sigma$, $\sigma^2$, $p$, $\bar{x}$, $\hat{p}$, $n$, $\mu_x$, $\mu_{\bar{x}}$, $\mu_{\hat{p}}$, $\sigma_x$, $\sigma_{\bar{x}}$, $\sigma_{\hat{p}}$).

Formulas/expressions you should understand when and how to use.

$$\mu = \sum_x xP(x) \ \ \ \ \ \sigma^2 = \sum_x (x-\mu)^2P(x) \ \ \ \ \ \sigma = \sqrt{\sum_x (x - \mu)^2P(x)}$$ $$z = \frac{x-\mu}{\sigma}$$

$$P(s) = \frac{n!}{s!(n-s)!}p^s(1-p)^{n-s}$$

$$\sigma_{\bar{x}} = \sigma_x/\sqrt{n} \ \ \ \ \ \ \ \sigma_{\hat{p}} = \sqrt{p(1-p)/n}$$