How to calculate the expectation of $XY$? Ask Question Asked 14 years, 3 months ago Modified 1 year, 10 months ago
probability - How to calculate the expectation of $XY$? - Mathematics ...
Are the statements "Expectation exists" "Expectation is finite" equivalent? If not, could someone please provide a counterexample. In case it's relevant, I don't know measure theory, but am confor...
The second term is such because $E (X)$ is a constant, and the expectation of a constant is the constant itself (same for the last term ($E (X))^2$) $=E (X^2)-2 (E (X))^2+ (E (X))^2=E (X^2)- (E (X))^2$
@Michael: Thanks! The tail sum formula is another way to computer expectation defined as in your comment.
Is there an exact or good approximate expression for the expectation, variance or other moments of the maximum of $n$ independent, identically distributed gaussian ...
Expectation of negative binomial distribution Ask Question Asked 5 years, 5 months ago Modified 3 years ago
3 A clever solution to find the expected value of a geometric r.v. is those employed in this video lecture of the MITx course "Introduction to Probability: Part 1 - The Fundamentals" (by the way, an extremely enjoyable course) and based on (a) the memoryless property of the geometric r.v. and (b) the total expectation theorem.
I understand how to define conditional expectation and how to prove that it exists. Further, I think I understand what conditional expectation means intuitively. I can also prove the tower property,
It seems like you're trying the "calculus route", however, when dealing with expectation of a variable with an exponent that is greater than 2, using Moment Generating Functions would be easier.