Introduction to Probability
4b. Conditional expectation
4. Expectation and variance
Conditional expectation as a random variable.
[Si] "Expected value" : Sect 5 "Conditional expected value" : Item
"The elementary definition"
.
[BT]
: Sect 2.6 "Conditioning" : Item "Conditional expectation" (pp. 104-),
and Sect 4.3 "More on conditional expectation and variance".
[GS]
: Sect 6.1 "Expected value of discrete random variables" : Item "Conditional expectation" (pp. 239-240).
Total (iterated) expectation.
[Si] "Expected value" : Sect 5 "Conditional expected value" : Items
"The general definition"
,
"Properties"
.
[BT]
: Sect 2.6 "Conditioning" : Item "Conditional expectation" (pp. 104-),
and Sect 4.3 "More on conditional expectation and variance".
[GS]
: Sect 6.1 "Expected value of discrete random variables" : Item "Conditional expectation" (pp. 239-240).
Martingales. Forecast revision.
[BT]
: Sect 4.3 "More on conditional expectation and variance".
[GS]
: Sect 6.1 "Expected value of discrete random variables" : Item "Martingales" (p. 241).
Expectation and independence.
[Si] "Expected value" : Sect 1 "Definition and properties" : Item
"Basic properties"
.
[BT]
: Sect 2.7 "Independence" : Item "Independence of random variables" (pp. 37-39).
[GS]
: Sect 6.1 "Expected value of discrete random variables" : Item "Independence" (pp. 233-234).
Expectation of geometric and negative binomial (or Pascal) random variables.
[BT]
: Sect 2.6 "Conditioning" : Example 2.17 (p. 106-); Sect. 5.1 "The Bernoulli process" : Item "The
k
-th arrival time" (p. 279-).
Back to syllabus