The Gateway to Computer Science Excellence
First time here? Checkout the FAQ!
x
+1 vote
200 views

suppose X and Y are random variables such that

E(X)=1 (Y)=2 V(X)=1 V(Y)=2 Cov(X,Y)=1

by using above values following expression are evaluated

E(X+2Y)=p

EXY)=q

Vat(X-2Y+1)=r

find pq+r

 

 

 

asked in Probability by Veteran (33.2k points)
recategorized by | 200 views

1 Answer

0 votes
IF X,Y are independent than  Cov(X,Y) $=$ 0  . Here its $\neq$ 0 . So we they are dependent .

E(X+2Y) = E(X) + 2E(Y) = 5 = p

Cov(X,Y) = E(XY) - E(X)E(Y)  on solving E(XY) = 3 =q .

Var(X - 2Y + 1) = Var(X) + 4Var(Y) + Var(1) + 2Cov(X,-2Y) + 2Cov(X,1) + 2C(Y,1)    [Var[constant]= 0 ]

Cov(X,Y) = 0 if X , Y are independent . So Cov (X,1) = 0 , Cov(Y) =0 .

                         = Var(X) + 4Var(Y) -4Cov(X,Y)       [ Cov(X,-Y) = -Cov(X,Y) ]

On putting the values we get  r=5

Therefore  pq+r = 20
answered by Boss (7.2k points)


Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true

28,982 questions
36,818 answers
91,195 comments
34,706 users