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Advice for Chapter 7 Be able to distinguish between a discrete random variable and a continuous random variable Understand how to find the expected value of a discrete random variable. o Expected value is the mean of the probability distribution. o X x i p (x i ) o Can also be represented as E(X) o Does not have to be a whole number Understand how to find the variance of a discrete random variable o 2 Var (X ) (x )2 P (x ) Understand how to find the standard deviation of a discrete random variable. o Var (X ) The probability distribution for a continuous random variable is defined in terms of a density curve. (Think Normal distributions). You must be able to work with transformations and combinations of random variables. o These rules apply to any random variables X and Y: a bX a b X 2a bX b 2 2 X X Y X Y o For independent random variables X and Y: 2 X Y 2 X 2Y More Advice o Do not assume normality. Make sure that normality is justified. o Watch out for variables that aren’t independent. You will not be able to add their variances. o Variances of independent variables add. Standard deviations DO NOT. o Variances of independent variables add, even when you are looking for the difference. o Do not write independent instances of a random variable with notation that looks like they are the same variable. Write X 1 X 2 X 3 instead of X X X . Calculator Functions o normalcdf (lowerbound, upperbound, mean, std dev) gives the probability a.k.a. area under the density curve If looking for area to the left of the curve, lowerbound = -1E99 If looking for area to the right of the curve, upperbound = 1E99 o Invnorm(area, mean, std dev) Returns x-values for given area Measures from the left of the curve Be sure you are reporting the correct area—always draw a picture