Consider a financial services salesperson whose annual salary consists of both a fixed portion of $25,000 and a variable portion that is a commission based on her sales performance. In particular, she estimates that her monthly sales commission can be represented by a random variable with mean $5000 and standard deviation $700.

Assuming that her sales commissions in different months are independent random variables, what is the standard deviation of her annual salary?

这是哪里的题啊？不会是gmat的吧，居然要用到 Markov stochastic process的性质。According to the theory of Markov stochastic process, when we add two independant normal distributions, the result is a normal distribution where the mean is the sum of the mean and the variance is the sum of the variances. So

for annual salary:

mean = 25,000 + 5,000 + ..... + 5,000 (there are totally 12 '5,000') = 85,000

variance = 700*700 + ........ + 700*700 (there are totally 12 such terms) = 12*490,000

standard deviation = square root of variance = 2*700*1.732