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Katie Rader Mathematics Englisch 69 Karten

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  1. 1Response vs Explanatory VariableResponse is the possible expected outcomes (dependent), Explanatory is the variable we try to see if it affects the response (independent).
  2. 2How far away from the IQR must an observation be in order for it to be considered an outlier (hint: box plots)3/2
  3. 3For a symmetric distribution, are robust or non-robust measurements better?Non-robust
  4. 4Robust MeasurementsMedian, IQR (not as influenced by outliers)
  5. 5Non-Robust MeasurementsMean, Std. Dev., Variance (Influenced by outliers)
  6. 6When mean < median, then your graph skews which way?Left
  7. 7If P(a * b) = P(a) * P(b), that tells us what?the probability of event a and the probability of event b are INDEPENDENT
  8. 8The general addition rule states that P(A or B) =P(A) + P(B) - P(A & B)
  9. 9P(A|B) is read as ___ in plain English"Probability of A, given that B has already happened"
  10. 10How would you find P(A & B) =P(A|B) * P(B)
  11. 11If we know what P(B|A), P(A), and P(B) is, then we can find P(A|B) with this formula:If we know what P(B|A), P(A), and P(B) is, then we can find P(A|B) with this formula:
  12. 12When given P(A|X), P(A|Y), and P(A|Z), the probability of A is...(P(A|X) * P(X)) + (P(A|Y) * P(Y)) + (P(A|Z) * P(Z))
  13. 13The General Variance Formula States...Var = Sum of all (probability of outcome) * (probability of outcome - mean)^2The General Variance Formula States...
  14. 14For some random variable (numerical and discrete) with unknown distribution, E(x) =Sum of all (outcome * probability of outcome)
  15. 15For some random variable (numerical and discrete) with an unknown distribution, std. deviation =the square root of (the general variance formula * sample size)
  16. 16What is the shorthand for Normal Distribution?N(μ, σ)
  17. 17What does a Z-Score describe?How many standard deviations away an observation is from the mean
  18. 18normalcdf or pnorm does what (technical/mathematical aspect)?Returns the area to the left of a given value x in the normal distribution. (1-pnorm for right tail)
  19. 19Write a pnorm command using the following data: mean = 50, std dev = 20, lower bounds = Bpnorm(B, 50, 20)
  20. 20What does Pnorm find?The percentage/percentile of observations that are worse than some given observation.
  21. 21Qnorm / Invnorm finds what?The inverse of the normalcdf / Pnorm function. Instead of inputting an observation to find percentile, you input a percentile to find observation.
  22. 22E(x) of a standard Bernoulli Distribution is what?P
  23. 23Std. Deviation of a standard Bernoulli Distribution is what?SQRT(P * (1-P))
  24. 24For a Bernoulli variable, what the probability of a "hit"? The probability of a "no hit"? (respectively).P; 1-P
  25. 25A geometric distribution is used to find what?Describes the chances of the first "hit" being on the nth observation.
  26. 26E(x) of a geometric distribution is what?1/P
  27. 27The std. dev of a geometric distribution is what?The std. dev of a geometric distribution is what?
  28. 28A Binomial Distribution is used to find what?To find the probability that k# of "hits" will happen within n# of trials.
  29. 29For a Binomial Distribution to be appropriate for a study, what requirements must the data qualify?Each trial must be: Independent, Have fixed number of trials, Outcome can only be "hit" or "no hit", and probability of "hit" is the same for each observation
  30. 30The mean and std. dev of a Binomal distribution is what? (respectively).np; SQRT(np * (1 - p)
    (n = # of trials, p = probability of "hit")
  31. 31The probability of observing k# of "hits" in n# of trials is given by this formula:The probability of observing k# of "hits" in n# of trials is given by this formula:
  32. 32is equal to...is equal to...is equal to...
  33. 33Pbinom gives what (mathematically)?Returns the area to the left of a given value q in the binomial distribution
  34. 34pbinom(k, n, p). What is k, n, and p respectively?k = total # of "hits", n = total # of observations, p = probability of a "hit"
  35. 35If in a binomial distribution, both np and n(1-p) are over 10, what does that mean?You can approximate the distribution using the normal distribution. I.e. you can use methods for the normal distribution (pnorm, qnorm, etc).
  36. 36A Negative Binomial Distribution describes what?The probability of observing the kth success on the nth observation.
  37. 37P(kth success on nth observation) = ?P(kth success on nth observation) = ?
  38. 38A Poisson Distribution is used to find what?The chances of a certain # of "hits" occurring in a large population over a certain unit of time.
  39. 39What variable is λPoisson parameter
  40. 40λ = ?λ is mean of a Poisson dist.
  41. 41How would you find the expected result of a Poisson parameter, given λ and number of "hits"How would you find the expected result of a Poisson parameter, given λ and number of "hits"
  42. 42Std. Dev of a Poisson Distribution is what?SQRT(λ)
  43. 43ppois finds what?The chance that a given number of "hits" will happen in a time frame, given the typical mean number of "hits"
  44. 44ppois(x, y). What should x equal? y? (respectively).x = number of "hits"; y = λ
  45. 45Z-Score is calculated as:Z-Score is calculated as:
  46. 46What is Standard Error? (not formula)The standard deviation of a sample; Measures uncertainty of point estimate
  47. 47What is the equation for Standard Error?What is the equation for Standard Error?
  48. 48What is a sampling distribution?It is a normal distribution where each observation is actually the mean value of a sample. I.e., what if we took the means of many samples and made that into a normal distribution.
  49. 49What is the z* value for a 99% confidence interval?2.58
  50. 50What is the z* value for a 95% confidence interval?1.96
  51. 51What is the formula for a confidence interval?What is the formula for a confidence interval?
  52. 52What is a type I error?Rejecting the Null Hypothesis when there isn't actually enough evidence to reject it.
  53. 53What is a type II error?Failing to reject the null hypothesis when we have enough evidence to reject it.
  54. 54What is a P-Value?A P-Value represents how likely it is that our study resulted the way it did, given we assume that the null hypothesis is true.
  55. 55If we have two numerical statistics that we want to compare, we can use:Poole Proportion
  56. 56In a Poole proportion, what is the "center" of phat1 - phat2?0
  57. 57What distribution do we use when we want to compare categorical data?Chi-Square Distribution
  58. 58How do we find P-Value of normal distribution?2*(1-Pnorm(phat, mean, SE))
  59. 59What is the standard error of phat1-phat2?What is the standard error of phat1-phat2?
  60. 60How do we find p-value of a chi-square?1-Pchisq(test stat, df)
  61. 61How do you find the df of a chi-square distribution?n-1
  62. 62How do you find test statistic of chi-square distribution?How do you find test statistic of chi-square distribution?
  63. 63how is the poole proportion between 2 phat values calculated?how is the poole proportion between 2 phat values calculated?
  64. 64How do we find p-value when working with a poole proportion?2*pnorm(phat1-phat2, 0, SE)
  65. 65What is the df in a t-distribution?n-1
  66. 66To find p-value of a t-distribution, what do you do?2*pt(test statistic, df)
  67. 67The test statistic of a t-distribution is calculated as what?(mean1-mean2)/SE
  68. 68SE of a t-distribution is calculated as what?SE of a t-distribution is calculated as what?
  69. 69—

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Beschreibung
Study guide for Discrete Structures Under Uncertainty class (statistics). Does not include answer key or practice questions.
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Katie Rader
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