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

Isuck at math ; ^; m a student solved this problem and said the answer is 3 feet. chase had a roll of ribbon that contained 7 7/8  feet of ribbon. he cut off one piece that was 3 5/8  feet long and another piece that was 1 1/4  feet from the roll. how much ribbon was left on the roll? is the student's answer reasonable? yes, the answer is reasonable. no, the answer is not reasonable. it should be about 2 feet. no, the answer is not reasonable. it should be about 13 feet. no, the answer is not reasonable. it should be about 4 feet.

The krasnapolski is a top-of-the-line hotel in amsterdam, the netherlands. among their many services, they rent bicycles to guests. the bicycle checkout is open 24 hours per day 7 days per week and has 50 bicycles on hand. on average, 10 guests request a bicycle each day, arriving completely randomly at all times of the day during the spring and summer seasons. guests keep bicycles for four days on average, with a standard deviation of two days. how long does a guest on average have to wait for a bike? a. approximately 24 hours b. approximately 0.033 hours c. approximately 4 days d. approximately 47 minutes

In which direction does the left side of the graph of this function point? a(x) = 3x - x2 + 4x - 2