The total time, measured in units of 100 hours, that a teenager runs her hair dryer over a period of one year is a continuous random variable X that has the density function below. Use the theorem below to evaluate the mean of the random variable Y = 69X² +43X, where Y is equal to the number of kilowatt hours expended annually. Theorem: The expected value of the sum or difference of two or more functions of a random variable X is the sum or difference of the expected values of the functions, as given by the formula below. E[g(X,Y) ±h(X,Y)] = E[g(X,Y)] ± E[h(X,Y)] f(x) = X, 4 1 9 Ō 0

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