By Geweke J., Tanizaki H.
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Extra resources for On Markov chain Monte Carlo methods for nonlinear and non-gaussian state-space models
2. Multiply k percent times the total number of numbers, n. 3a. If your result from Step 2 is a whole number, go to Step 4. If the result from Step 2 is not a whole number, round it up to the nearest whole number and go to Step 3b. 3b. Count the numbers in your data set from left to right (from the smallest to the largest number) until you reach the value from Step 3a. This corresponding number in your data set is the kth percentile. 4. Count the numbers in your data set from left to right until you reach that whole number.
Find the average of the data set, . To find the average, add up all the numbers and divide by the number of numbers in the data set, n. 2. For each number, subtract the average from it. 3. Square each of the differences. 4. Add up all the results from Step 3. 5. Divide the sum of squares (Step 4) by the number of numbers in the data set, minus one (n – 1). If you do Steps 1 through 5 only, you have found another measure of variability, called the variance. 6. Take the square root of the variance.
784. 973. Two phrases to remember: “at-least” means that number or higher; “at-most” means that number or lower. For example the probability that X is at least 2 is P(X ≥ 2); the probability that X is at most 2 is P(X ≤ 2). The Expected Value and Variance of the Binomial The mean of a random variable is the long-term average of its possible values over the entire population of individuals (or trials). It’s found by taking the weighted average of the x-values multiplied by their probabilities. The mean of a random variable is denoted by .