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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. Is used to describe probability in a continuous probability distribution. For example - you can't say that the probability of a man being six feet tall is 20% - but you can say he has 20% of chances of being between five and six feet tall. Probabilit






2. Is data that can take only two values - usually represented by 0 and 1.






3. In Bayesian inference - this represents prior beliefs or other information that is available before new data or observations are taken into account.






4. Cov[X - Y] :






5. In particular - the pdf of the standard normal distribution is denoted by






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






7. Involves taking measurements of the system under study - manipulating the system - and then taking additional measurements using the same procedure to determine if the manipulation has modified the values of the measurements.






8. Is the probability of an event - ignoring any information about other events. The marginal probability of A is written P(A). Contrast with conditional probability.






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






10. A measurement such that the random error is small






11. 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.






12. A numerical measure that describes an aspect of a population.






13. To prove the guiding theory further - these predictions are tested as well - as part of the scientific method. If the inference holds true - then the descriptive statistics of the new data increase the soundness of that






14. Rejecting a true null hypothesis.






15. Is the set of possible outcomes of an experiment. For example - the sample space for rolling a six-sided die will be {1 - 2 - 3 - 4 - 5 - 6}.






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






17. A scale that represents an ordinal scale such as looks on a scale from 1 to 10.






18. Given two jointly distributed random variables X and Y - the marginal distribution of X is simply the probability distribution of X ignoring information about Y.






19. Error also refers to the extent to which individual observations in a sample differ from a central value - such as






20. Is a function that gives the probability of all elements in a given space: see List of probability distributions






21. Patterns in the data may be modeled in a way that accounts for randomness and uncertainty in the observations - and are then used for drawing inferences about the process or population being studied; this is called






22. Is denoted by - pronounced 'x bar'.






23. When you have two or more competing models - choose the simpler of the two models.






24. Is the probability of some event A - assuming event B. Conditional probability is written P(A|B) - and is read 'the probability of A - given B'






25. Where the null hypothesis is falsely rejected giving a 'false positive'.






26. Is one that explores the correlation between smoking and lung cancer. This type of study typically uses a survey to collect observations about the area of interest and then performs statistical analysis. In this case - the researchers would collect o






27. Is the length of the smallest interval which contains all the data.






28. Are written in corresponding lower case letters. For example x1 - x2 - ... - xn could be a sample corresponding to the random variable X.






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






30. (or just likelihood) is a conditional probability function considered a function of its second argument with its first argument held fixed. For example - imagine pulling a numbered ball with the number k from a bag of n balls - numbered 1 to n. Then






31. E[X] :






32. A group of individuals sharing some common features that might affect the treatment.






33. Summarize the population data by describing what was observed in the sample numerically or graphically. Numerical descriptors include mean and standard deviation for continuous data types (like heights or weights) - while frequency and percentage are






34. Gives the probability distribution for a continuous random variable.






35. In the long run - as the sample size increases - the relative frequencies of outcomes approach to the theoretical probability.






36. The probability of the observed value or something more extreme under the assumption that the null hypothesis is true.






37. Probability of accepting a false null hypothesis.






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






39. Can be - for example - the possible outcomes of a dice roll (but it is not assigned a value). The distribution function of a random variable gives the probability of different results. We can also derive the mean and variance of a random variable.






40. Have no meaningful rank order among values.






41. 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.






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






43. Long-term upward or downward movement over time.






44. 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






45. (or atomic event) is an event with only one element. For example - when pulling a card out of a deck - 'getting the jack of spades' is an elementary event - while 'getting a king or an ace' is not.






46. (e.g. ? - b) are commonly used to denote unknown parameters (population parameters).






47. A variable describes an individual by placing the individual into a category or a group.






48. 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






49. When info. in a contingency table is re-organized into more or less categories - relationships seen can change or reverse.

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50. (also called statistical variability) is a measure of how diverse some data is. It can be expressed by the variance or the standard deviation.