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.
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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 ($E (X))^2$) $=E (X^2)-2 (E (X))^2+ (E (X))^2=E (X^2)- (E (X))^2$