{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Homework Solutions 04 - (W4150 Intro to Probability and...

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

View Full Document Right Arrow Icon
Solutions to Homework #4 (W4150 ‘Intro to Probability and Statistics’, S04) Sec. 4.1. (1) In this problem we have to integrate joint distribution density function multiplied by x with respect to both x and y - but one should be very careful when setting limits for integration. You may choose any of these variables to be ’free’ in the sense that it can go from –a to a , but the second variable must be restricted with respect to the inequality x 2 + y 2 < a 2 . So if you take, for example, y as a free variable, you’ll end up with E[X] = 0 2 2 1 1 2 2 2 2 2 2 2 2 2 2 = ° ± ² ³ ´ µ · ¸ ¹ ¹ º » - - · ¸ ¹ ¹ º » - = ¼ ¼ ¼ - - - - - dy y a y a a xdxdy a a a y a y a a a π π Sec.4.1. (4) Assigning weights of 3 w and w for a head and tail, respectively, we obtain P(H) = ¾ and P(T) = ¼. The sample space for the experiment is S = {HH, TH, HT, TT}. Now if X represents the number of tails that occur in two tosses of the coin, we have P(X=0) = P(HH) = (3/4)(3/4) = 9/16; P(X=1) = P(HT) + P(TH) = 2(3/4)(1/4) = 3/8; P(X=2) = P(TT) = (1/4)(1/4) = 1/16.
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