Midterm 1, Winter 06Moulinath BanerjeeUniversity of MichiganFebruary 22, 2006Announcement:The exam carries 30 points but the maximum you can score is 25.(1) IfXandYare two uncorrelated random variables, are they necessarily independent? On theother hand, if they are independent, are they necessarily uncorrelated? Justify your answers.(6)(2) LetXandYbe independent standard normal random variables. SetU= (3X+ 4Y)/5 andV= (4X-3Y)/5.(i) Find the joint density of (U, V) and also the marginal densities. (8)(ii) Show thatU2+V2is distributed like an exponential random variable with parameter1/2. (4)(3) Two helicopters land independently of each other on the plane.
This is the end of the preview.
access the rest of the document.
Probability theory, University of Michigan, Moulinath Banerjee, exponential random variable, uncorrelated random variables