. _._. Mm.u_l1._ . .i . L
5 a 4 The Moment-Generating Function Technique
Theorem 5.4-1 If X1, - - - ,Xn are independent random variable with respective moment~
generating functions M X1. (t), i: = 1, - - - ,n, then the momentgenerating function of Y =
23:
5 Random Functions Associated with Normal Distri-
butions
(NTheorem 5.5-1 If X1, - ,Xn are mutually independent normal variables with means
m, - ~ it and variances of, - - ,0? respectively, then Y = 21:1 CiXi has the normal
distribution n n
N(thMz-,ZCCT)-
Chapter 5
Contents
3 Several Random Variables
3.1 pmf, pdf, cdf, marginals, conditionals, expectation, independence, etc. . . .
4 The Moment-Generating Function Technique
5 Random Functions Associated with Normal Distributions
6 The Central Limit Theorem
Chapter 5
Contents
1 Functions of One Continuous Random Variable
1.1 Transformations .
2 Transformations of Two Random Variables
2
3
9 1 Functions of One Continuous Random Variable
Recall that a random variable is continuous if its cdf FX (3:) is a conti
._ u. . _
Chapter 7 '
Contents
3 Condence Interval for Proportions 1
3.1 Condence Interval for a Population Proportion p . 3
3 Condence Interval for Proportions
Like population mean, the proportion of a population is also an important quantity of
the popu
_ ._._._ ._._u-_.J._. _ _
2.1 Condence Intervals for the Difference of Two Means
Paired Samples
By considering the dierence in measurements within each pair, we change the two-sample
problem to the one-sample problem. Therefore, we can use the one-sa
Chapter 7
Contents
1 Condence Intervals for Means 2
1.1 Condence Intervals for population mean a (0'? is known) . 4
1.2 Condence Intervals for population mean ,u (0'2 is unknown) . 8
2 Condence Intervals for the Difference of Two Means 12
2.1 Condence Int
2 Transformations of Two Random Variables
Change-ofVariables Technique.
Let X1,X2 be two continuous type random variables with joint pdf f(:c1,:c2). If Y1 =
u1(X1, X2), Y2 = u2(X1, X2) has the singlevalued inverse X1 = 111(Y1, Y2), X2 2 1120/1, Y2),
then