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The formula computes the probability that at least one of the Aievents happens. The probability of getting exactly one of the Aievents is similarly computed by: Xk i=1 Pr(Ai)−2 Xk i<j Pr(Ai∩Aj)+3 Xk i<j<c Pr(Ai∩Aj∩Ac)−... ±kPr(A 1 ∩A 2 ∩A 3 ∩...∩Ak) Important result Probability of any (Boolean) expression involving events A,B ...
The regression line of y on x has equation y = a + bx, where b = , and a = – b. Using the coding x = hX + m, y = gY + n, the regression line for Y on X is found by writing ̅. gY + n instead of y, and hX + m instead of x in the equation of the regression line of y on x, ⇒ gY + n.
A common problem in statistics is that of detecting and representing the relationship that exists (if any) between two random variables X and Y; for instance, height and weight, income and intelligence quotient (IQ), ages of husband and wife at marriage,
AS MATHS - STATISTICS REVISION NOTES. PLANNING AND DATA COLLECTION. • PROBLEM SPECIFICATION AND ANALYSIS. What is the purpose of the investigation? What data is needed? How will the data be used? • DATA COLLECTION. How will the data be collected? How will bias be avoided? What sample size is needed? PROCESSING AND REPRESENTING.
18.05 Introduction to Probability and Statistics (S22), Class 19 Slides: NHST III. pdf. 74 kB. 18.05 Introduction to Probability and Statistics (S22), Class 20 Slides: Comparison of Frequentist and Bayesian Inference. pdf. 29 kB. 18.05 Introduction to Probability and Statistics (S22), Class 21 Slides: Exam 2 Review.
The subjects of Statistics and Probability concern the mathematical tools that are designed to deal with uncertainty. To be more precise, these subjects are used in the following contexts: To understand the limitations that arise from measurement inaccuracies. To find trends and patterns in noisy data. To test hypothesis and models with data.
Here are the formulas for sums of squares. We will see that there are simpler formulas when we know the sample means and sample variances for each of the agroups.
