# Increasing the vertical dispersion increases the

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Increasing the vertical dispersion increases the slope o Increasing the horizontal dispersion flattens the line o correlation=slope when we measure X and Y in Stdevs Larger correlation -> larger combined stdev -> Lower Z-Score (if combined mean does not change) -> lower percentile Probability Distribution Generated model against which we compare data against o Random variable is a random draw from a distribution, dice roll Expected value is the probability-weighted average of its possible outcomes (mean) o Calculated as the sum of all possible values each multiplied by the probability of its occurrence Variance of a random variable is the probability-weighted average of its squared deviation from its mean Standard deviation = probability-weighted average distance from the mean Binomial Setting: The probability of a success, call it p, is the same for each observation o Stdev Shortcut:
o X = number of successes in n tries, with success probability p SAXBY formula SAXBY = Standard deviation of aX+bY This formula relates the variance of a combination aX+bY (such as a portfolio return) to the standard deviations of X and Y and their correlation. The formula holds for any numbers a and b. It does not require a+b=1.