180ahw6 - MATH 180A Introduction to Probability Homework...

Info icon This preview shows page 1. Sign up to view the full content.

MATH 180A – Introduction to Probability Homework 6 (due 11/20/06) 1. Consider an urn with 1 red, 2 green and 3 blue balls. 5 balls are drawn from that urn without replacement. Let X be the number of red balls picked and Y the number of green balls picked. Find the joint distribution of X and Y . 2. Consider an urn with 1 red, 2 green and 3 blue balls. 100 balls are drawn from that urn with replacement. What is the probability that: (a) There are 15 red, 35 green and 50 blue balls? (b) All balls are of the same color? (c) There are more blue balls than red and green balls together? 3. Consider X and Y random variables with joint probability density function f ( x, y ) = C ( y - x ) e - y , 0 < x < y, y (0 , ) . (a) Are X and Y independent? (b) Compute C . (c) Compute E ( X ), var( X ), E ( Y ), var( Y ). (d) Compute the marginal densities of X and Y . 4. Same as above with f ( x, y ) =
Image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: f ( x, y ) = C x 2 y (1-y 2 ) , x ∈ (-1 , 1) , y ∈ (0 , 1) . 5. Factory A produces a certain type of resistor. The resistor lifetime has the exponential distribution. The average resistor lasts 1,000 hours. Suppose we buy several resistors from factory A to design a couple of circuits. (a) For circuit 1, we set them in parallel, so that circuit 1 works if any of the resistors work. Compute the minimum number of resistors we need to buy in order for circuit 1 to last at least 10,000 hours with probability 95%. (b) For circuit 2, we set them in series, so that circuit 2 works if all of the resistors work. Compute the maximum number of resistors we can buy in order for circuit 2 to last at least 100 hours with probability 95%....
View Full 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