Jane's savings account starts every month with an amount X, that is uniformly distributed between $1000...

 

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Jane's savings account starts every month with an amount X, that is uniformly distributed between $1000 and $1500. Her expenses during the month can be modeled as a random variable S, which is uniformly distributed between $400 and $800, and this amount is independent of X. At the end of the month, her account balance Y is equal to the starting balance reduced by her expenses. (a) Find the LMS estimate ŝ of her expenses S, given her account balance y at the end of the month. (15 pts) (b) Find the MSE of the LMS estimate ŝ of her expenses S, given her account balance y at the end of the month. (10 pts) Jane's savings account starts every month with an amount X, that is uniformly distributed between $1000 and $1500. Her expenses during the month can be modeled as a random variable S, which is uniformly distributed between $400 and $800, and this amount is independent of X. At the end of the month, her account balance Y is equal to the starting balance reduced by her expenses. (a) Find the LMS estimate ŝ of her expenses S, given her account balance y at the end of the month. (15 pts) (b) Find the MSE of the LMS estimate ŝ of her expenses S, given her account balance y at the end of the month. (10 pts)

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