Practice qn Quant.Methods

[narayananvenkat]

David..

Please help me in soving this with details.
y=1 y=2 y=3
x=1 0.05 0.05 0.10
x=2 0.05 0.10 0.15
x=3 0.15 0.15 0.20


Use the above joint probability distribution to answer the foll:
1. The expected value of Y is closest to

a. .2
b. 1
c. 2.3
d. 2.2

2. Suppose Y is equal to 2, the probability that X is equal to 1 is closest to

a. .05
b. .25
c. .17
d. .2

3. The variance of X is closest to

a. .54
b. .61
c. .67
d. .74

Thanks

 

[David Harper CFA FRM]

venkat,

I input into XLS here:
http://sheet.zoho.com/public/btzoho/0919-prob

http:///learn.bionicturtle.com/images/forum/0919_prob.png

This question is *great* for giving practice to conditional vs. unconditional ... I would recommend "using" this problem to meditate on conditional/unconditional/joint...note the variance is E(X^2) - (E(X))^2, which comes in handy often!

Thanks, David

 

[djdejna]

I suppose that Q2 is about P(X=1|Y=2) so the answer is a) => .05. Right?

Reg
Sebastian

 

[David Harper CFA FRM]

Hi Sebastian, not quite (that's why this is a handy exercise)

joint probability P(X=1,Y=2) = 0.05
unconditional P(Y = 2) = 0.3
conditional or marginal P(X=1|Y=2) = =.05/.30 = 0.17

David

 

[djdejna]

OK, i get it.
It's X=1 when Y=2, not X=1 and Y=2.

Thx
Sebastian