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Understand what is meant by random variables, and discrete versus continuous quantitative random variables.
Understand what is meant by the probability distribution of a discrete random variable.
Understand what is meant by a population distribution and a sampling distribution.
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).
Know how to compute probabilities using the probability distribution of a discrete random variable.
Know how to compute probabilities using the probability distribution of a continuous random variable.
Know how to compute probabilities using a normal probability distribution (with statdistributions.com).
Know how to derive a sampling distribution using the five-step method.
Know how to use the binomial distribution to derive the sampling distribution of \(\hat{p}\).
Know how to find/compute the mean and standard deviation of \(\bar{x}\) and \(\hat{p}\).
Know how to find the interval that has a probability of approximately 0.95 of containing \(\bar{x}\) or \(\hat{p}\).
Understand what it means to say that a statistic is unbiased.
Understand what is meant by the standard error of a statistic.
Understand what is implied by the central limit theorem.
Why do we divide by \(n-1\) rather than \(n\) when computing \(s^2\)?
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.
\[ \mu = \sum_x xP(x) \ \ \ \ \ \sigma^2 = \sum_x (x-\mu)^2P(x) \ \ \ \ \ \sigma = \sqrt{\sum_x (x - \mu)^2P(x)} \] \[ z = \frac{x-\mu}{\sigma} \]
\[ P(s) = \frac{n!}{s!(n-s)!}p^s(1-p)^{n-s} \]
\[ \sigma_{\bar{x}} = \sigma_x/\sqrt{n} \ \ \ \ \ \ \ \sigma_{\hat{p}} = \sqrt{p(1-p)/n} \]