410Hw05ans.pdf - STAT 410 Homework#5(due Friday March 29 by 4:00 p.m Spring 2019 A Stepanov Please include your name with your last name underlined your

410Hw05ans.pdf - STAT 410 Homework#5(due Friday March 29 by...

This preview shows page 1 - 4 out of 12 pages.

STAT 410 Homework #5 (due Friday, March 29, by 4:00 p.m.) Spring 2019 A. Stepanov Please include your name ( with your last name underlined ) , your NetID, and your section number at the top of the first page. No credit will be given without supporting work. 1. Every month, the government of Neverland spends G million dollars purchasing guns, B million dollars purchasing butter, and P million dollars purchasing pants. Assume that ( G , B , P ) jointly follow a N 3 ( , ) , a 3- dimensional multivariate normal distribution with μ = 315 175 151 , = 1600 200 136 200 625 136 136 136 400 . a) Find the probability that the government of Neverland spends more on guns than twice the amount it spends on butter during a given month. That is, find P ( G > 2 B ) . Want P ( G > 2 B ) = P ( G – 2 B > 0 ) = ? G – 2 B has Normal distribution, E ( G – 2 B ) = G – 2 B = 315 – 2 175 = 35 , Var ( G – 2 B ) = 1600 200 136 1 1 2 0 200 625 136 2 136 136 400 0           = 1 2000 1450 136 2 0 = 4900 . P ( G – 2 B > 0 ) = P ( Z > 0 35 4900   ) = P ( Z > 0.50 ) = 0.3085 .
Image of page 1
b) Find the probability that the government of Neverland spends more on guns than it spends on butter and pants together during a given month. That is, find P ( G > B + P ) . Want P ( G > B + P ) = P ( G – B – P > 0 ) = ? G – B – P has Normal distribution, E ( G – B – P ) = G B P = 315 – 175 – 151 = 11 , Var ( G – B – P ) = 1600 200 136 1 1 1 1 200 625 136 1 136 136 400 1           = 1 1936 689 400 1 1 = 3025 . P ( G – B – P > 0 ) = P ( Z > 0 11 3025   ) = P ( Z > 0.20 ) = 0.4207 . c) Find the probability that the government of Neverland exceeds the $600 million spending limit during a given month. That is, find P ( G + B + P > 600 ) . G + B + P has Normal distribution, E ( G + B + P ) = G + B + P = 315 + 175 + 151 = 641 , Var ( G + B + P ) = 1600 200 136 1 1 1 1 200 625 136 1 136 136 400 1           = 1 1264 289 128 1 1 = 1681 . P ( G + B + P > 600 ) = P ( Z > 600 641 1681 ) = P ( Z > – 1.00 ) = 0.8413 .
Image of page 2
2 – 5. The Weibull distribution has many applications in reliability engineering, survival analysis, and general insurance. Let > 0, > 0. Consider the probability density function δ 1 β δ , δ δ ; β β x e x x f , x > 0, zero otherwise.
Image of page 3
Image of page 4

You've reached the end of your free preview.

Want to read all 12 pages?

  • Spring '08
  • AlexeiStepanov

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

Ask Expert Tutors You can ask You can ask ( soon) You can ask (will expire )
Answers in as fast as 15 minutes