Lecture-23 - Lecture 23 Some topics from 10.1 Fact...

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

View Full Document Right Arrow Icon
Lecture 23. Some topics from 10.1 Fact. Expectation is linear: E( aX ) = a E( X ) for any constant a and any random variable X and E( X + Y ) = E( X ) + E( Y ) for any random variables X and Y . Thus, for any constants a i and random variables X i , E( a 1 X 1 + . . . + a n X n ) = a 1 E( X 1 ) + . . . + a n E( X n ) . Comment. Of course, for the statements in the Fact to be a meaningful, it is necessary that E( X ), E( Y ) and all the E( X i ) exist. In the following, we will deal only with random variables that have and expected value.) Question. Give an example of a discrete random variable that has no expected value. Example. If a die is rolled n times, the expected sum of the rolls is n time the expected outcome of a single roll. More generally, if any experiment with numerical outcomes is repeated n times, the expected sum of the outcomes is n times the expected outcome of a single trial. Example 10.3.
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 11/29/2011 for the course MATH 3355 taught by Professor Britt during the Spring '08 term at LSU.

Ask a homework question - tutors are online