Introduction to Probability
4c. Variance
4. Expectation and variance
Variance and standard deviation: equivalent definitions.
[Si] "Expected value" : Sect 2 "Variance and higher moments" : Item
"Definition"
.
[BT]
: Sect 2.4 "Expectation, mean and variance" (pp. 13-17).
[GS]
: Sect 6.2 "Variance of discrete random variables" (pp. 257-258).
Basic properties. Linear transformations.
[Si] "Expected value" : Sect 2 "Variance and higher moments" : Item
"Properties"
.
[BT]
: Sect 2.4 "Expectation, mean and variance" : Item "Properties of mean and variance" (pp. 86-).
[GS]
: Sect 6.2 "Variance of discrete random variables" (p. 259).
Standard score.
[Si] "Expected value" : Sect 2 "Variance and higher moments" : Item
"Properties"
.
[GS]
: Sect 6.2 "Variance of discrete random variables" (p. 264).
Chebyshev's inequality.
[Si] "Expected value" : Sect 2 "Variance and higher moments" : Item
"Chebyshev's inequality"
.
[GS]
: Sect 8.1 "Law of large numbers for discrete random variables" (pp. 305-306).
Center, spread and the best constant prediction.
[Si] "Expected value" : Sect 2 "Variance and higher moments" : Item "Center and spread revisited" (find it after
"Distance"
).
[BT]
: Sect 4.6 "Least squares estimation" (p. 241).
[GS]
: Sect 6.2 "Variance of discrete random variables" (p. 266).
Variance of uniform random variables.
[Si] "Expected value" : Sect 2 "Variance and higher moments" : Item "Examples and special cases" (find it after
"Properties"
).
[BT]
: Sect 2.4 "Expectation, mean and variance" : Item "Mean and variance of some common random variables" (p. 88-).
Variance and convolution.
[BT]
: Sect 2.7 "Independence" : Item "Independence of random variables".
[GS]
: Sect 6.2 "Variance of discrete random variables" (pp. 259-260).
Variance of binomial and Poisson random variables.
[Si] "Bernoulli trials" : Sect 2 "The binomial distribution" : Item
"Moments"
.
[BT]
: Sect 2.7 "Independence" : Item "Variance of the sum..." : Example 2.20;
also "Problems to Chapter 2" : Problem 24 (p. 123).
[GS]
: Sect 6.2 "Variance of discrete random variables" (p. 261 binomial; p. 262 Poisson).
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