As in an earlier exercise, we assume that the random variables θ and x are described by a joint pdf which is uniform on the triangular set defined by the constraints 0≤x≤1 , 0≤θ≤x . a) find an expression for the conditional mean squared error of the lms estimator given that x=x , valid for x∈[0,1] . express your answer in terms of x using standard notation.

1. according to the internal revenue service, the mean tax refund for the year 2007 was $2,708. assume the standard deviation is $650 and that the amounts refunded follow a normal probability distribution. a. what percent of the refunds are more than $3,000? b. what percent of the refunds are more than $3,000 but less than $4,000? c. what percent of the refunds are less than $2,000?