Let θ and x be jointly continuous nonnegative random variables. a particular value x of x is observed and it turns out that θ||=− , for ≥0.
the following facts may be useful: for an exponential random variable with parameter , we have =1/ and =1/
(a) the lms estimate (conditional expectation) of θ is
(b) the conditional mean squared error e[(θ−θ^lms)2|x=x] is
(c) the map estimate of θ is
(d) the conditional mean squared error e[(θ−θ^map)2|x=x] is