# Homework Help: Expectation and Standard Deviation(SD)

1. Nov 10, 2009

### helix999

Hi

I have a question.

Let X1 & X2 be stochastic variables and X1<=X2, then can we say E[X1]<=E[X2] or SD[X1]<=SD[X2]? why or why not?

Thanks!

2. Nov 10, 2009

### lanedance

what do you think?

and by X1 <=X2, does this mean every outcome of X1 is <= every outcome of X2?

3. Nov 10, 2009

### helix999

yeah, the given condition is for every outcome.
I think E[x1]<=E[x2] but no idea abt std deviation. i dont know if i am correct.

4. Nov 10, 2009

### clamtrox

Could you prove it?

If you think that the relation does not always hold for standard deviation, could you perhaps find variables X and Y for which this is the case?

5. Nov 10, 2009

### lanedance

its always a good place to start at the defintions (either discrete or continuous will work)

from the definitions, E[X1]<= E[X2] shoudl be obvious

for the standard deviation, building on clamtrox's argument, it might help to consider the dsicrete variable pdf:
P(X2= x2) = 1, if x2 = b
P(X2= x2) = 0, otherwise
whats the standard deviation of this "random" variable?

6. Nov 10, 2009

consider X1 and X2 with distributions
[tex]
\begin{tabular}{l c c c c c}
x & 10 & 20 & 30 & 40 & 50 \\
p(x) & .80 & .1 & .07 & .02 & .01\\
\end{tabular}

7. Nov 10, 2009

### helix999

zero.

8. Nov 10, 2009

### lanedance

yep... just to show for a random variabe the SD, can be quite separate from the mean.... hopefully you can thnk of a RV with all lesser outcomes, but non-zero SD

though i hope i haven't simplified too much, what exactly do you mean by a stochastic variable here...?

Last edited: Nov 10, 2009
9. Nov 10, 2009

### helix999

ok i got the examples when SD[x1]<=SD[x2]. But when SD[x1>=Sd[x2]?