Question

Need help :) Q in following post

Answer 1

Any help or hints are appreciated :) Lots!

Answer 2

Explain E(X|Y)... expected value of X given Y is what?
If the question is as is, does this mean the answer has a variable?

Answer 3

sloooow computer

Answer 4

I'm just guessing here...
when Y=0, E(X) = 0
when Y=1, E(X) = 1

so, E(X|Y)=Y

Answer 5

Ah, your prev post makes sense i think.

Answer 6

as for Covariance
cov(X,Y) = E[XY] - E[X]*E[Y]

E[X] & E[Y] should be 0.5 ..... not sure how you calculate E[XY]

Answer 7

You agree that E[X] = E[Y] = 0.5?

Answer 8

boo. the Y=0 didn't show here

Answer 9

I thought Cov(X,Y) should be numerical value...
there is a 50% chance E(X)=0, there is a 50% chance E(X)=1,\[E(X)= 0.5*0\ +\ 0.5*1=0.5\]

Answer 10

You know, that makes sense. Ok. that works .

Answer 11

for E(XY)
when Y is 0, XY is just 0,so E[XY] is 0


when Y is 1, XY=X...\[ X= \sim \mathcal{N}(1,1)\]so E[XY]=1

so I think E[XY] is also 0.5, although not sure.

Answer 12

Ok. all help is appreciated, esp to help me see it different ways.

Answer 13

tricky problem, eh?

Answer 14

:) so my guess for cov(X,Y) = 0.5-0.25= 0.25

Answer 15

I think I was wrong about E[XY] = 0.5 ...you can't just take the probabilities of the expected values and add them up here...
When Y=0, XY= 0
When Y=1, XY= ∼N(1,1)
graphing,