The discussion revolves around the properties of expectation and standard deviation in relation to stochastic variables, specifically examining the implications of the condition X1 ≤ X2 on E[X1] and SD[X2].
There is ongoing exploration of definitions and properties related to expectation and standard deviation. Some participants suggest starting with definitions to clarify the relationships, while others are considering specific examples to test their hypotheses. Multiple interpretations of the implications of the stochastic variables are being discussed.
Participants are discussing the definitions of stochastic variables and the conditions under which the relationships between expectation and standard deviation hold. There is a focus on both discrete and continuous cases, and some participants express uncertainty about the implications of their assumptions.
helix999 said:I think E[x1]<=E[x2]
helix999 said:but no idea abt std deviation. i don't know if i am correct.
lanedance said: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?
<br /> <br /> ok i got the examples when SD[x1]<=SD[x2]. But when SD[x1>=Sd[x2]?statdad said:consider X1 and X2 with distributions
<br /> \begin{tabular}{l c c c c c}<br /> x & 10 & 20 & 30 & 40 & 50 \\<br /> p(x) & .80 & .1 & .07 & .02 & .01\\<br /> \end{tabular}