Counting
Problem:
Multiplication Rule
Example:((X23) P(0) P(1) P(2)
=
2 Tree
Diagraph
f(x)
x
+
+
xP(x)
P(3)
+
F(3)
=
SCDFtatich phan caf(x)-pdf
xP(X)
doan-8 -> X (
probability -> P(X...) phai
BD:P(x > a)
1
=
-
convert ve
-Probability try goc:x1+X2=1
hanh
P(x,y) x
=
Discrete Random Variable
x
4
x
(x2)
this:
wo
CDF-F(X)
P(x a) 1
Xa)
1
=
Continuous Random Variable
pdf f(x)
-
↑
-
=
endebai khona,ChoSanF(X)
Normal Distribution (Special
x
follow
->
ngegenham f(xe
Continuous Random Variable)
Normal Dist
(parameter M, 64
KhngenphaKapeingtheinte
P(X(a) P(z za)
hin;butb ic phai da vidang phir tap
=
I
E
F(a)
-
=
Nen X-N(M, 62)
probabilitydensipeace
t the
P(X1a)
P(X2a)
-
=
To
dang
P(X(a)
P(a<X(b) P(X<b)
-Probability eng
the x
Hi
Detin
P(X = a)
Probability Density function (pdf)
->
curve
f(x)
Za:
*
Trabang
P(X) a) P(z =
Z
za) 1
=
p(a(X(b) P(xxb)
=
dedice
-
-
P(z
gia tri.P(z_u)
za)
P(X= a) P(z =zb)
=
-
P(z
za)
=