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Ch 6.2 Transforming and Combining Random Variables Remember… The effects of adding / subtracting a constant value to each observation Adds that value to the center and location (mean, median, quartiles, percentiles) Does not change the shape or spread (range, IQR, standard deviation) The effects of multiplying / dividing a constant value to each observation Multiplies that value to the center and location (mean, median, quartiles, percentiles) Multiplies that value to the spread (range, IQR, standard deviation) Does not change the shape of the distribution (skew or normal) New… The effects of a linear transformation (+/- and x/÷) Y = a + bX Adds and Multiplies that value to the center and location (mean µY = a + bµX) Multiplies that value to the spread (standard deviation σY = lblσX) Does not change the shape of the distribution (skew or normal) We can also combine two different random variables (T = X ± Y) so that the following is true The expected value E(T) = the sum of the means: µT = µX ± µY The variance = the sum of the variances: = + *only when independent *Independent events are events where knowing whether the first event happens tells us nothing about the second event (so they don’t effect each other)