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QM Exam 2
QM Chapter 6, 7, 9, 11
| Term | Definition |
|---|---|
| random variable | value is based on the outcome of a random event |
| discrete random variable | we can list all the outcomes of this random variable |
| continuous random variable | a random variable that can take on any value (possibly bounded on one or both sides) |
| probability model | for both discrete and continuous variables, the collection of all the possible values and the probabilities associated with them |
| parameter | a numerically valued attribute of the probability model |
| expected value | found by multiplying each possible value of the random variable by the probability that it occurs and then summing all those products |
| standard deviation | describes the spread in the model and is the square root of the variance |
| variance | the expected value of the squared deviations from the mean |
| Addition Rule for Expected Values of Random Variables | the expected value of the sum (or difference) of random variables is the sum (or difference) of their expected values |
| Addition Rule for Variances of (Independent) Random Variables | the variance of the sum or difference of two independent random variables is the sum of their individual variances |
| correlation | we divide the covariance by each of the standard deviations to get this |
| Bernoulli trials | there are only two possible outcomes (success and failure) for each trial; the probability of success, denoted p, is the same on every trial (the prob of failure, 1-p often denoted q); the trials are independent |
| the 10% condition | Bernoulli trials must be independent. in theory, we need to sample from a population that's infinitely big. However, if the population is finite, it's still okay to proceed as long as the sample is smaller than 10% of the population. |
| discrete Uniform distribution, U[1, ..., n] | over a set of n values, each value has probability 1/n |
| geometric probability model | uses probability to answer the question "how long (how many trials) will it take to achieve the first success?" These are completely specified by one parameter, p, the probability of success |
| binomial random variable | whenever the random variable of interest is the number of successes in a series of bernoulli trials; takes two parameters to define this probability model: the number of trials, n, and the probability of success, p |
| Poisson model | a discrete model often used to model the number of arrivals of events such as customers arriving in a queue or calls arriving into a call center |
| 68-95-99.7 Rule | In a normal model, 68% of values fall within one standard deviation of the mean, 95% fall within two standard deviations of the mean, and 99.7% fall within 3 standard deviations of the mean |
| normal distributions | "bell-shaped curves," appropriate models for distributions whose shapes are unimodal and roughly symmetric |
| Standard normal distribution/model | The normal distribution with mean 0 and standard deviation 1 |
| Continuous random variable | The distribution of its probability can be shown skin a curve called the probability density function |
| Normal Probability density function | The curve we use to work with the normal distribution f(x) |
| Normal percentiles | Corresponding to a z-score gives the percentage of values in a standard normal distribution found at that z-score or below |
| Normal probability plot | A display to help assess whether a distribution of data is approximately normal. If the plot is early straight, the data satisfy the nearly normal condition |
| Success/failure condition | A binomial model is approximately normal if we expect at least 10 successes and 10 failures |
| Continuity correction | Adjustment made when we use a continuous model to model a set of discrete events |
| Cumulative distribution function | A function for a continuous probability model that gives the probability of all values below a given value |
| Sampling error | The variability we expect to see from sample to sample, although sampling variability is a better term |
| Sampling distribution | The distribution of all the sample proportions that would arise from all possible samples of the same size with a constant probability of a "success" |
| Independence assumption | The sampled values must be independent of each other |
| Sample size assumption | The sample size, n, must be large enough |
| Standard error | Whenever we estimate the standard deviation of a sampling distribution |
| Confidence intervals | Statements that don't tell us everything we might want to know, but they're the best we can do |
| One-proportion z-interval | A confidence interval for the true value of a proportion |
| Margin of error | A confidence interval, the extent of the interval on either side of the estimate. Typically the product of a critical value from the sampling distribution and a standard error from the data |
| Critical value | The number of standard errors to move away from the estimate to correspond to the specified level of confidence. Denoted z*, usually found from a table or with technology |
| Central limit theorem | States that the sampling distribution model of the sample mean and proportion from a random sample is approximately normal for large n, regardless of the distribution of the population, as long as the observations are independent |
| Standard erreor | An estimate of the standard deviation of a statistics sampling distribution based on the data |
| Students t | A family of distributions indexed by its degrees of freedom. Unimodal, symmetric, and bell-shaped, but generally have fatter tails and a narrower center the the normal model |
| Degrees of freedom | Family of related distributions that depend on a parameter |
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