Random Vari X, Y both discrete and take values of 1 or 2. Probability for (X∩Y)

Statistics
Tutor: None Selected Time limit: 1 Day

a. Find E(Y2), E(X2

 b. Find  σ2 x σy c. Find P(X=1|Y=1), P(X=2|Y=2) (for this one I got 1/4 on both, I'm stuck on a and b). Much help is appreciated!

y=1y=2
x=11/41/8
x=23/81/4

Feb 19th, 2015

Probability for (X∩Y)

        y=1  y=2 

x=1  1/4  1/8  3/8

x=2  3/8  1/4  5/8

         5/8  3/8  1

E(y) =5/8*1 +3/8 *2 = 11/8

E(X) = 3/8*1+5/8*2 =13/8

a)

E ( y2 ) = 5/8*12+3/8* 22 = 17/8

E ( x2 ) = 3/8*12+5/8* 22 = 23/8

b)

Sigmax2 = E ( x2) –[E(x)]2 = 23/8 -169/64 = 184/64-169/64 = 15/64

Sigmay2 = E ( y2) –[E(y)]2 = 17/8 -121/64 = 136/64-121/64 = 15/64

c)

P( x=1 | y=1 ) = 1/ 4 /(5/8) = 2/8*(8/5)=2/5

P( x=2 | y=2 ) = 1/ 4 /(3/8) = 2/8*(8/3)=2/3


Feb 19th, 2015

Studypool's Notebank makes it easy to buy and sell old notes, study guides, reviews, etc.
Click to visit
The Notebank
...
Feb 19th, 2015
...
Feb 19th, 2015
Mar 27th, 2017
check_circle
Mark as Final Answer
check_circle
Unmark as Final Answer
check_circle
Final Answer

Secure Information

Content will be erased after question is completed.

check_circle
Final Answer