MA519_JAN06

MA519_JAN06 - QUALIFYING EXAMINATION JANUARY 2006 MATH 519...

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

View Full Document Right Arrow Icon
QUALIFYING EXAMINATION JANUARY 2006 MATH 519 - Prof. Dasgupta NOTE : 1. ANSWER TWO QUESTIONS FROM EACH GROUP. IF YOU ANSWER MORE THAN TWO QUESTIONS, ONLY THE FIRST TWO YOU HAVE ANSWERED WOULD BE GRADED. THE OTHERS WILL NOT GET GRADED. 2. STANDARD NORMAL TABLE MAY BE REQUIRED FOR SOME PROBLEMS. Group A 1. The birthdays of 5 people are known to fall in exactly 3 calendar months. What is the probability that exactly two of the 5 were born in January ? 2. Coupons are drawn, independently, with replacement, one at a time, from a set of 10 coupons. Find, explicitly, the expected number of draws a) until the first drawn coupon is drawn again; b) until a duplicate occurs. 3. Let N be a positive integer. Choose an integer at random from { 1 ,...,N } .L e t E be the event that your chosen random number is divis- ible by 3, and divisible by at least one of 4 and 6, but not divisible by 5. Find, explicitly, lim N →∞ P ( E
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.

This document was uploaded on 01/25/2012.

Page1 / 2

MA519_JAN06 - QUALIFYING EXAMINATION JANUARY 2006 MATH 519...

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