HW4_Spring11_Sol - ELEC210 Spring 2011 Homework-4-Solution...

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
ELEC210 Spring 2011 Homework-4-Solution 1. The random variable X has cdf as shown in the figure below: (a) What type of random variable is X? (b) Find the following probabilities: , , , , , . Solution(16 ): (a) (4 ) The cdf is neither continuous nor piece-wise constant, so it s mixed type. (b) (12 ) , , , , , . 2. A point is selected at random inside a square defined by . Assume the point is equally likely to fall anywhere in the square. Let the random variable Z be given by the minimum of the two coordinates of the point. (a) Find the sample space S of the coordinates of the point and the sample space of Z, . (b) Show the mapping from S to . (c) Find the region in the square corresponding to the event . (d) Find the cdf of Z. (e) Use the cdf to find: .
Image of page 1

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

View Full Document Right Arrow Icon
Solution(16 ): (a) (3 ) , . (b) (3 ) The two segments as shown by the bold black curve in S correspond to point a in (c) (3 ) The region corresponding to the event is shown by the blue area. (d) (3 ) . (e) (4 ) , , , .
Image of page 2
Image of page 3
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