Introduction to Probability
5. Limit theorems
5a. Weak law of large numbers.
[Si] "Random samples" : Sect 2 "The sample mean and the law of large numbers" : Item
"The weak law of large numbers"
.
[BT]
: Sect 7.2 "The weak law of large numbers".
[GS]
: Sect 8.1 "Law of large numbers for discrete random variables".
5b. Central limit theorem.
[Si] "Random samples" : Sect 5 "The central limit theorem" : Item
"Statement of the theorem"
.
[BT]
: Sect 7.4 "The central limit theorem".
[GS]
: Sect 9.2 "Central limit theorem for discrete independent trials".
5c. Normal approximation to binomial distribution.
[Si] "Random samples" : Sect 5 "The central limit theorem" : Items
"Normal approximation"
,
"Normal approximation to the binomial distribution"
,
"Normal approximation to the Poisson distribution"
.
[BT]
: Sect 7.4 "The central limit theorem" : Items "Approximations based on the cenral limit theorem", "The DeMoivre-Laplace approximation to the binomial".
[GS]
: Sect 9.1 "Central limit theorem for Bernoulli trials".
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