Let be two discrete random variables having finite moments (I assume this means ). Show that
a) if , then
b) if , then
HINT: You may consider the variable .
Again, with so much to do in so little time, I need help.
Let be two discrete random variables having finite moments (I assume this means ). Show that
a) if , then
b) if , then
HINT: You may consider the variable .
Again, with so much to do in so little time, I need help.
It means something rather stronger than that, in fact far stronger than is needed here, all you need is that they have finite first moments.
The detail of thia depends on the type of course you are doing, but in essense this depends on the definite integral of a positive function being positive.Show that
a) if , then
Part b) follows from part a) by introducing the RV , and the linearity of the expectation operator.b) if , then
HINT: You may consider the variable .
Again, with so much to do in so little time, I need help.
CB
You can't do statistics without integration (rather you cannot do statistics using only discrete probability distributions other than in a half arsed manner), what I was trying to suggest is that the proof would be slightly more subtle if you were doing a course using measure theory.
CB