Screenshot 2018-09-30 at 00.25.43.png - What the above demonstrates is two basic rules for expectations operators regardless of whether random variables

# Screenshot 2018-09-30 at 00.25.43.png - What the above...

• Notes
• 1

This preview shows page 1 out of 1 page. #### You've reached the end of your free preview.

Want to read the whole page?

Unformatted text preview: What the above demonstrates is two basic rules for expectations operators regardless of whether random variables are discrete or continuous: 1) E(a) = a “The expected value of a constant is a constant” 2) E(bX) = bE(X) “The expected value of a constant times a random variable is equal to the constant times the expected value of the random variable” More generally let X Y and Z be three random variables eanch with their own density functions and let W = aX + bY + cZ, then E(W) = aE(X) + bE(Y) + cE(Z). 2. g(X) = (Ii-EGO)i i = 2, .. Functions of this form yield “i’th moments about the mean”. The metric here is the i’th power of that of the original distribution so that if f(x) relates to incomes measured in \$US then the i’th moment about the mean is measured in (\$US)i. Sometimes the i’th root of g(X) is employed since it yields a measure of the appropriate characteristic in terms of the original units of the distribution. Furthermore to make distributions measured under different metrics comparable the ﬁlnction g(X) deﬂated by the appropriate power of E(X) (provided it is not 0) is considered, providing a metric free comparator. The second moment (i = 2) is of particular interest1 since as the variance (frequently represented as 02 or V(X), its square root 0 is referred to as the standard deviation) it provides a measure of how spread out a distribution is. Of particular interest here is ...
View Full Document

### What students are saying

• 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.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• 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.

Dana University of Pennsylvania ‘17, Course Hero Intern

• 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.

Jill Tulane University ‘16, Course Hero Intern  