HW10_Problem_Set - ORIE 3500/5500 Fall Term 2008 Assignment...

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

View Full Document Right Arrow Icon
ORIE 3500/5500 Fall Term 2008 Assignment 10 Note that the due date is Monday, November 24 , at 1:00 pm you need to mention your section number on the top of your answer script. 1. [5 + 5 + 5 = 15 pts] The points ( X, Y ) obtained by the students of a course in the two prelims is modeled by a bivariate normal distribution with parameters μ X = 60 , μ Y = 75 , σ X = 18 , σ Y = 12 , ρ = 0 . 75. Maximum possible points in both the prelims are 100. (a) If the final score consists of 40% of prelim 1 and 60% of prelim 2, then find the distribution of the final score. (b) If there are 300 students enrolled for the course, how many of them are expected to score more than 70 in prelim 1? (c) If 50 students score 70 in prelim 1, how many of them are expected to score more than 80 in prelim 2? 2. [5 + 5 = 10 pts] Suppose X Poisson ( λ ) and α (0 , 1). (a) Apply the Markov inequality for the random variable Y s = e - sX to get an upper bound for P ( X < αλ ). (b) Minimize the bound obtained in (a) with respect to
Background image of page 1

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

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

Page1 / 2

HW10_Problem_Set - ORIE 3500/5500 Fall Term 2008 Assignment...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online