Let y1, y2, y3, and y4 be random variables and let a1, a2, a3, and a4 be

Question:

Let y1, y2, y3, and y4 be random variables and let a1, a2, a3, and a4 be real numbers. Show that the following relationships hold for finite discrete distributions.

(a) E(a1y1 + a2y2 + a3) = a1E(y1) + a2E(y2) + a3.

(b) Var(a1y1 + a2y2 + a3) = a2 1Var(y1) + a2 2Var(y2) for y1 and y2 independent.

(c) Cov(a1y1 + a2y2, a3y3 + a4y4) = 2 i=1

4 j=3 aiajCov(yi, yj ).

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Answer rating: 100% (QA)

Answered By

Somshukla Chakraborty

I have a teaching experience of more than 4 years by now in diverse subjects like History,Geography,Political Science,Sociology,Business Enterprise,Economics,Environmental Management etc.I teach students from classes 9-12 and undergraduate students.I boards I handle are IB,IGCSE, state boards,ICSE, CBSE.I am passionate about teaching.Full satisfaction of the students is my main goal. I have completed my graduation and master's in history from Jadavpur University Kolkata,India in 2012 and I have completed my B.Ed from the same University in 2013. I have taught in a reputed school of Kolkata (subjects-History,Geography,Civics,Political Science) from 2014-2016.I worked as a guest lecturer of history in a college of Kolkata for 2 years teaching students of 1st ,2nd and 3rd year. I taught Ancient and Modern Indian history there.I have taught in another school in Mohali,Punjab teaching students from classes 9-12.Presently I am working as an online tutor with concept tutors,Bangalore,India(Carve Niche Pvt.Ltd.) for the last 1year and also have been appointed as an online history tutor by Course Hero(California,U.S) and Vidyalai.com(Chennai,India).

4.00+ 2+ Reviews 10+ Question Solved

Related Book For book-img-for-question