Let θ1 , θ2 , w1 , and w2 be independent standard normal random variables. we obtain two observations, x1=θ1+w1,x2=θ1+θ2+w2. find the map estimate θ^=(θ^1,θ^2) of (θ1,θ2) if we observe that x1=1 , x2=3 . (you will have to solve a system of two linear equations.)

Ben wants to play a carnival game that costs $2. in his pocket he has 5 red tickets worth 35 cents each, and 15 blue tickets worth 10 cents each. which of the following systems of inequalities correctly represents the constraints on the variables in this problem? let represent the red tickets and b represent the blue tickets.

In 2009, there were 1570 bears in a wildlife refuge. in 2010, the population had increased to approximately 1884 bears. if this trend continues and the bear population is increasing exponentially, how many bears will there be in 2018?

Ateam of runners is needed to run a 1 2 -mile relay race. if each runner must run 1 4 mile, how many runners will be needed?