Below is the definition of the law of total expectation from Wiki. The first equation states that for any $X, Y$ on the same probability space, then \begin {equation} E (X) = E (E (X|Y)) \end {equation}
Law of total expectation: how to relate $E(X) = E(E(X|Y))$ to $E(X ...
I think the law of iterated expectations is a generalization of the law of total expectations, in your wording. But just as you knew (from the Wikipedia page) they are just the two names of the same thing.
Are the law of iterated expectation and the law of total expectations ...
I quote (emphasis mine) from the wikipedia definition: The proposition in probability theory known as the law of total expectation, ..., states that if X is an integrable random variable (i.e., a
PLE 7.25 The Law of Total Expectation Geometric Random Variables Use the law of total expectation to obtain the expected value of a geometric random variable with parameter p. Solution Let X ~G (p). We recall that X represents the number of trials up to and including he first success in repeated Bernoulli trials with success probability p.
The law of total expectation says something analogously: E [B] = E (E [B|A]] (Note that E [B|A] is a random variable since it is a function of A). Derive E [Y] from Problem 1 again using the law of total expectation.
Step 1 Solution :- The law of total expectation states that for any random variables X and Y, \ [E [X] = E [E [X|...
Solved Use the law of total expectation to compute the - Chegg