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CLEP General Mathematics: Probability And Statistics

Subjects : clep, math
Instructions:
  • Answer 50 questions in 15 minutes.
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  • Match each statement with the correct term.
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This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it re-enforces your understanding as you take the test each time.
1. In particular - the pdf of the standard normal distribution is denoted by






2. (or multivariate random variable) is a vector whose components are random variables on the same probability space.






3. A variable has a value or numerical measurement for which operations such as addition or averaging make sense.






4. Is the function that gives the probability distribution of a random variable. It cannot be negative - and its integral on the probability space is equal to 1.






5. Probability of accepting a false null hypothesis.






6. Var[X] :






7. Failing to reject a false null hypothesis.






8. The errors - or difference between the estimated response y^i and the actual measured response yi - collectively






9. Are two related but separate academic disciplines. Statistical analysis often uses probability distributions - and the two topics are often studied together. However - probability theory contains much that is of mostly of mathematical interest and no






10. Is a measure of the 'peakedness' of the probability distribution of a real-valued random variable. Higher kurtosis means more of the variance is due to infrequent extreme deviations - as opposed to frequent modestly sized deviations.






11. Are usually written with upper case calligraphic (e.g. F for the set of sets on which we define the probability P)






12. ?r






13. Is a set of entities about which statistical inferences are to be drawn - often based on random sampling. One can also talk about a population of measurements or values.






14. Is often denoted by placing a caret over the corresponding symbol - e.g. - pronounced 'theta hat'.






15. In number theory - scatter plots of data generated by a distribution function may be transformed with familiar tools used in statistics to reveal underlying patterns - which may then lead to






16. Where the null hypothesis fails to be rejected and an actual difference between populations is missed giving a 'false negative'.






17. Have both a meaningful zero value and the distances between different measurements defined; they provide the greatest flexibility in statistical methods that can be used for analyzing the data






18. A pairwise independent collection of random variables is a set of random variables any two of which are independent.






19. (pdfs) and probability mass functions are denoted by lower case letters - e.g. f(x).






20. Is the probability of two events occurring together. The joint probability of A and B is written P(A and B) or P(A - B).






21. Is a function of the known data that is used to estimate an unknown parameter; an estimate is the result from the actual application of the function to a particular set of data. The mean can be used as an estimator.






22. Is a measure of its statistical dispersion - indicating how far from the expected value its values typically are. The variance of random variable X is typically designated as - - or simply s2.






23. Uses patterns in the sample data to draw inferences about the population represented - accounting for randomness. These inferences may take the form of: answering yes/no questions about the data (hypothesis testing) - estimating numerical characteris






24. Because variables conforming only to nominal or ordinal measurements cannot be reasonably measured numerically - sometimes they are grouped together as






25. Used to reduce bias - this measure weights the more relevant information higher than less relevant info.






26. Also called correlation coefficient - is a numeric measure of the strength of linear relationship between two random variables (one can use it to quantify - for example - how shoe size and height are correlated in the population). An example is the P






27. Is a parameter that indexes a family of probability distributions.






28. Is a sample and the associated data points.






29. Is its expected value. The mean (or sample mean of a data set is just the average value.






30. Of a group of numbers is the center point of all those number values.






31. A numerical measure that describes an aspect of a sample.






32. The probability distribution of a sample statistic based on all the possible simple random samples of the same size from a population.






33. A numerical facsimilie or representation of a real-world phenomenon.






34. Samples are drawn from two different populations such that the sample data drawn from one population is completely unrelated to the selection of sample data from the other population.






35. Have meaningful distances between measurements defined - but the zero value is arbitrary (as in the case with longitude and temperature measurements in Celsius or Fahrenheit)






36. Given two jointly distributed random variables X and Y - the conditional probability distribution of Y given X (written 'Y | X') is the probability distribution of Y when X is known to be a particular value.






37. Are usually written in upper case roman letters: X - Y - etc.






38. Design of experiments - using blocking to reduce the influence of confounding variables - and randomized assignment of treatments to subjects to allow unbiased estimates of treatment effects and experimental error. At this stage - the experimenters a






39. Is that part of a population which is actually observed.






40. Working from a null hypothesis two basic forms of error are recognized:






41. Is used in 'mathematical statistics' (alternatively - 'statistical theory') to study the sampling distributions of sample statistics and - more generally - the properties of statistical procedures. The use of any statistical method is valid when the






42. Can refer either to a sample not being representative of the population - or to the difference between the expected value of an estimator and the true value.






43. Describes a characteristic of an individual to be measured or observed.






44. Gives the probability of events in a probability space.






45. Have no meaningful rank order among values.






46. To find the average - or arithmetic mean - of a set of numbers:






47. Statistics involve methods of organizing - picturing - and summarizing information from samples or population.






48.






49. Changes over time that show a regular periodicity in the data where regular means over a fixed interval; the time between repetitions is called the period.






50. S^2