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.
What is the expectation of $ X^2$ where $ X$ is distributed normally? Ask Question Asked 14 years, 3 months ago Modified 10 years, 10 months ago
statistics - What is the expectation of $ X^2$ where $ X$ is ...
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.
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,
This is the Law of Total Expectation. The proof is as follows: $$ \begin {align} E [E [X|Y]] &= E \left [ \sum_ {x} x \cdot P (X = x | Y) \right] \ &= \sum_y \left ...
Expectation of sample variance Ask Question Asked 5 years, 2 months ago Modified 2 years ago
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Expectation of normal c.d.f. of a normal random variable Ask Question Asked 2 years, 5 months ago Modified 2 years, 5 months ago
expectation - What is the expected value of a probability density ...