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- https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Mostly_Harmless_Statistics_(Webb)/05%3A_Discrete_Probability_Distributions/5.08%3A_Chapter_5_FormulasDiscrete Distribution Variance: σ 2 = ∑(x i 2 ∙P(x i )) – μ 2 Geometric Distribution: P(X = x) = p ∙ q (x – 1) , x = 1, 2, 3, … Binomial Distribution: P(X = x) = n C x ·p x ·q (n-x ) , x = 0, 1, 2, … ...Discrete Distribution Variance: σ 2 = ∑(x i 2 ∙P(x i )) – μ 2 Geometric Distribution: P(X = x) = p ∙ q (x – 1) , x = 1, 2, 3, … Binomial Distribution: P(X = x) = n C x ·p x ·q (n-x ) , x = 0, 1, 2, … , n Hypergeometric Distribution: P(X = x) = \(\frac{a C_{x} \cdot {}_b C_{n-x}}{ _{N} C_{n}}\) Unit Change for Poisson Distribution: New μ = old μ(\(\frac{\text { new units }}{\text { old units }}\)) Poisson Distribution: P(X = x) = \(\frac{e^{-\mu} \mu^{x}}{x !}\)
- https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Mostly_Harmless_Statistics_(Webb)/02%3A_Organizing_Data/2.03%3A_Graphical_DisplaysThe shape of the histogram will be the same for the relative frequency distribution and the frequency distribution; the height, though, is the proportion instead of frequency. You can have your output...The shape of the histogram will be the same for the relative frequency distribution and the frequency distribution; the height, though, is the proportion instead of frequency. You can have your output default to a new worksheet, or select the circle to the left of Output Range, click into the box to the right of Output Range and then select one blank cell on your spreadsheet where you want the top left-hand corner of your table and graph to start.
- https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Mostly_Harmless_Statistics_(Webb)/04%3A_Probability/4.01%3A_IntroductionMore important questions that probability can help with are your chances that the car you are buying will need more maintenance, your chances of passing a class, your chances of winning the lottery, o...More important questions that probability can help with are your chances that the car you are buying will need more maintenance, your chances of passing a class, your chances of winning the lottery, or your chances of catching a deadly virus. The bottom sideway V assumes that a blue marble was drawn on the first draw, and then the second marble drawn can be either red or blue.
- https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Mostly_Harmless_Statistics_(Webb)/02%3A_Organizing_Data/2.02%3A_Tabular_DisplaysWhen creating frequency distributions, it is important to note that the number of classes that are used and the value of the first class boundary will change the shape of, and hence the impression giv...When creating frequency distributions, it is important to note that the number of classes that are used and the value of the first class boundary will change the shape of, and hence the impression given by, the distribution.
- https://stats.libretexts.org/Workbench/Statistics_for_Behavioral_Science_Majors/03%3A_Probability/3.02%3A_Three_Types_of_ProbabilityThe sample space is S = {1, 2, 3, 4, 5, 6}. The event A is that you want is to get a 4, and the event space is A = {4}. Thus, in theory the probability of rolling a 4 would be P(A) = 1/6 = 0.1667.
- https://stats.libretexts.org/Workbench/Statistics_for_Behavioral_Science_Majors/04%3A_Discrete_Probability_Distributions/4.03%3A_Geometric_DistributionsThe geometric distribution is P(X = x) = p ∙ q (x – 1) , x = 1, 2, 3, … where x is the number of trials up to the first success that you are trying to find the probability for, p is the probability of...The geometric distribution is P(X = x) = p ∙ q (x – 1) , x = 1, 2, 3, … where x is the number of trials up to the first success that you are trying to find the probability for, p is the probability of a success for one trial and q = 1 – p is the probability of a failure for one trial.
- https://stats.libretexts.org/Workbench/Statistics_for_Behavioral_Science_Majors/05%3A_Continuous_Probability_Distributions/5.02%3A_Uniform_DistributionThe probability is found by taking the area between two points within the rectangle formed from the x-axis, between the endpoints a and b, the length, and f(x) = 1/(b-a), the height. When working with...The probability is found by taking the area between two points within the rectangle formed from the x-axis, between the endpoints a and b, the length, and f(x) = 1/(b-a), the height. When working with continuous distributions it is helpful to draw a picture of the distribution, then shade in the area of the probability that you are trying to find. a) First plug in the endpoints a = 0 and b = 15 into the PDF to get the height of the rectangle.
- https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Mostly_Harmless_Statistics_(Webb)/11%3A_Analysis_of_Variance/11.02%3A_Pairwise_Comparisons_of_Means_(Post-Hoc_Tests)How to determine which means are significantly different from each other, if the ANOVA indicates rejecting the null hypothesis, using the Bonferroni Test.
- https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Mostly_Harmless_Statistics_(Webb)/05%3A_Discrete_Probability_Distributions/5.06%3A_Poisson_DistributionThe formula for the Poisson distribution is P(X = x) = \(\frac{e^{-\mu} \mu^{x}}{x !}\), where e is a mathematical constant approximately equal to 2.71828, x = 0, 1, 2, … is the number successes that ...The formula for the Poisson distribution is P(X = x) = \(\frac{e^{-\mu} \mu^{x}}{x !}\), where e is a mathematical constant approximately equal to 2.71828, x = 0, 1, 2, … is the number successes that you are trying to find the probability for, μ is the mean number of a success over one interval of time, space, volume, etc. The “old” would be the original stated mean and units and the “new” is the units from the question.
- https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Mostly_Harmless_Statistics_(Webb)/07%3A_Confidence_Intervals_for_One_PopulationDeveloping confidence intervals based on a sample for a single population.
- https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Mostly_Harmless_Statistics_(Webb)/zz%3A_Back_Matter/10%3A_Index
