2.2.2 Conditional Expectation

Question 1

what is conditional expectation?

Answer 1

A conditional expected value is the expected value of a random variable X
where only a portion of the values of X
are used. That portion is defined by a conditional range of X.

Question 2

what does conditional expectation look for the discrete case?

Question 3

what does conditional expectation look for the continuous case?

Answer 3

E[X | j ≤ X ≤ k] = integrate from j to k of x * f(x)dx over P( j ≤ X ≤ k)

Question 4

what are the key differences in expected value and conditional expectation?

Answer 4

expected values use unconditional probabilities and cover the entire range of X while conditional expected values use conditional probabilities and cover the conditional range of X