REGRESSION ANALYSIS M 384G
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This 1 page Class Notes was uploaded by Reyes Glover on Sunday September 6, 2015. The Class Notes belongs to M 384G at University of Texas at Austin taught by Staff in Fall. Since its upload, it has received 11 views. For similar materials see /class/181462/m-384g-university-of-texas-at-austin in Mathematics (M) at University of Texas at Austin.
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Date Created: 09/06/15
CONDITIONAL MEANS AND VARIANCES PART II M 384G374G MORE ON CONDITIONAL MEANS Summary of Part 1 The marginal mean of a random variable Y is the weighted average of the conditional means when conditioned on a second random variable X This says EY ZPrxEY lX x X discrete all vazum ofX or EY fXxE Y l xdx X continuous where fXx is the probability density function pdf of X Note 1 There are analogous results for conditioning on more than one variable 2 The analogous result for sample means is 7 A second related relationship between marginal and conditional means for populations Consider EYlX as a new random variable U as follows Randomly pick an x from the distribution of X The new rv U has value EYlX x Example Y height X sex Randomly pick a person from the population in question E Y lX female if the person is female EY lX male if the person is male Consider the expected value of this new random variable e g the expected value of the mean height for the sex of a randomly selected person from the given population In this case we would expect EU to depend on the proportion of the population which is of each sex
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