Examples for Ch.4.1
EX. 1
EX. 2
Examples for Ch. 4.2
EX.1
a) Find Cov(x, y)
b) Find Corr(x, y)
Examples for Ch. 4.4
EX1.
Let X1, X2 have the joint p.d.f.
f(x1,x2)=2, 0<x1<x2<1.
Let us consider Y1=X1/X2, and Y2=X2. What is the joint p.d.f. of Y1 and Y2?
Examples for Ch. 4.5
EX.1
EX. 2 (Example 4.5-1). Let X1 and X2 be two independent random variables resulting
from two carst of an unbiased die. That is, X1, X2 is a random sample of size n=2 from
a distribution with p.m.f f(x)=1/6, x=1,2,…,6.
1. E(X1), E(X2)
2. Var(X1), Var(X2)
3. E(X1X2)
4. E[(X1-μ1)(X2-μ2)]
EX. 3 (Example 4.5-2). Let X1, X2, X3 be a random sample from a distribution with
p.d.f. f ( x)  e  x , 0  x  
1. The joint p.d.f of X1,X2,X3
2. P(0<X1<1, 2<X2<3, 3<X3<7)
Examples for Ch. 4.6
EX. 1
EX. 2
Examples for Ch. 5.2
EX. 1
EX. 2 (From EX. 1)
EX. 3 ( Inside-Out problem)
Examples for Ch. 5.3
EX. 1
EX. 2