For a random variable x, a new random variable y can be created by applying a li

Question

For a random variable x, a new random variable y can be created by applying a linear transformation y = a + bx, where a and b are constants. If the random variable x has mean mu Subscript xx and standard deviation sigma Subscript xx, then the mean, variance and standard deviation of y are given by the following formulas. mu Subscript y Baseline equals a plus b mu Subscript xy=a+bxsigma squared Subscript y Baseline equals b squared sigma squared Subscript x2y=b22xsigma Subscript y Baseline equals |b| sigma Subscript x y=|b|x

The mean annual salary for employees at a company is $31,000. At the end of the year, each employee receives a $5000 bonus and a 9% raise (based on salary). What is the new mean annual salary (including the bonus and raise) for the employees?

Explanation / Answer

here new salary Y =5000+1.09X

therefore new mean annual salary E(Y) =5000+0.09*E(X) =5000+1.09*31000=$38790

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