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Homework Help: Expectation and Standard Deviation(SD)

  1. Nov 10, 2009 #1

    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?

    Looking forward to some reply

  2. jcsd
  3. Nov 10, 2009 #2


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    what do you think?

    and by X1 <=X2, does this mean every outcome of X1 is <= every outcome of X2?
  4. Nov 10, 2009 #3
    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.
  5. Nov 10, 2009 #4
    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?
  6. Nov 10, 2009 #5


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    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?
  7. Nov 10, 2009 #6


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    consider X1 and X2 with distributions
    \begin{tabular}{l c c c c c}
    x & 10 & 20 & 30 & 40 & 50 \\
    p(x) & .80 & .1 & .07 & .02 & .01\\
  8. Nov 10, 2009 #7
  9. Nov 10, 2009 #8


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    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
  10. Nov 10, 2009 #9
    ok i got the examples when SD[x1]<=SD[x2]. But when SD[x1>=Sd[x2]?
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