# ws731 - Rob Bayer Math 55 Worksheet Independence of...

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

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Rob Bayer Math 55 Worksheet July 31, 2009 Independence of R.V.’s, Chebyshev’s Inequality 1. Determine whether each of the following pairs of random variables are independent or not: (a) X=“number of heads,” Y=“number of tails,” when three fair coins are flipped (b) X=“sum of dice,” Y=“value of first die” when two fair dice are tossed (c) X =“sum of dice mod 2”, Y=“value of first die” when two fair dice are tossed 2. Suppose two professors are co-teaching a course and trying to write a midterm. If they have a bank of k 2 problems to choose from and each (independently) chooses k problems they want to put on the exam, what is the expected number of problems chosen by both professors? Hint: make a r.v.’s X i ,Y i for whether each professor chose problem i or not. 3. Consider the experiment in which you flip a fair coin 3 times. Determine V ( X ) and σ ( X ) for each of the following: (a) X =“number of heads” (b) X =“longest consecutive run of the same result”...
View Full Document

## This note was uploaded on 09/10/2009 for the course MATH 55 taught by Professor Strain during the Summer '08 term at Berkeley.

Ask a homework question - tutors are online