Test 2 & Solutions - Probability and Statistics Course...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Probability and Statistics Course 92.386 Test 2 Time: 1 hour 30 minutes Please answer any five ofthe following six questions. Eachquestion isworth5 points Note: Numerical answers without supporting statements willnot be given credit. 1. A coin is biased so that heads is twice as likely to occur as tails. For 3 independent tosses of the coin, a. determine the probability distribution function (Pdf) of the random variable X, the total number of heads b. find the probability of getting at mosttwo heads 2. Each tile of an experimental airplane is supposed to be filled to a pressure of 4Opsi" Let X denotethe actualpressurefor the righttireand Y denote the actualpressurefor the lefttire, SupposeX and Y are random variables withjoint density given by: fx,y (x, y) = k (x 2 '·I ); 30 <x < 50, 30<y < 50 a. Findthe probability that both tiresare underfilled. b. AreX and Y independent? Justify your answer' 3. If thejoint probability density function of random variables X andY isgivenby: fx,y (x, y) = 24 Y (l-x-y); for 0 < x < 1, 0 <y < 2 and0 elsewhere, It;
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern