Probability &
Statistics
Conditional
PDF on an
Event
Multiple
Continuous
Random
Variables
Conditional
PDF on a
Random
Variable
1/25
Probability & Statistics
Continuous Random Variables 2
TRAN Hoang Tung
NGUYEN Minh Huong
NGUYEN Mai Chung
University of Science and Technology of Hanoi (USTH)
September 24, 2019
Probability &
Statistics
Conditional
PDF on an
Event
Multiple
Continuous
Random
Variables
Conditional
PDF on a
Random
Variable
2/25
The Course So Far
What we have learnt?
Probability &
Statistics
Conditional
PDF on an
Event
Multiple
Continuous
Random
Variables
Conditional
PDF on a
Random
Variable
2/25
The Course So Far
What we have learnt?
Fundamental probability
Probability &
Statistics
Conditional
PDF on an
Event
Multiple
Continuous
Random
Variables
Conditional
PDF on a
Random
Variable
2/25
The Course So Far
What we have learnt?
Fundamental probability
Discrete random variables
Probability &
Statistics
Conditional
PDF on an
Event
Multiple
Continuous
Random
Variables
Conditional
PDF on a
Random
Variable
2/25
The Course So Far
What we have learnt?
Fundamental probability
Discrete random variables
Continuous random variables: PDF, CDF, expectation
Probability &
Statistics
Conditional
PDF on an
Event
Multiple
Continuous
Random
Variables
Conditional
PDF on a
Random
Variable
3/25
1
Conditional PDF on an Event
Conditional PDF
Total Expectation Theorem
CDF: Revisited
2
Multiple Continuous Random Variables
Joint PDF
Marginal PDF
Joint CDF
3
Conditional PDF on a Random Variable
Conditional PDF
Conditional Expectations
Independence
Probability &
Statistics
Conditional
PDF on an
Event
Conditional
PDF
Total
Expectation
Theorem
CDF: Revisited
Multiple
Continuous
Random
Variables
Conditional
PDF on a
Random
Variable
4/25
1
Conditional PDF on an Event
Conditional PDF
Total Expectation Theorem
CDF: Revisited
2
Multiple Continuous Random Variables
3
Conditional PDF on a Random Variable
Probability &
Statistics
Conditional
PDF on an
Event
Conditional
PDF
Total
Expectation
Theorem
CDF: Revisited
Multiple
Continuous
Random
Variables
Conditional
PDF on a
Random
Variable
5/25
Conditional PDF on an Event
Definition
A random variable
X
is called
continuous
if there is a PDF
f
X
such that
P
(
X
∈
B
) =
Z
B
f
X
(
x
)
dx
Probability &
Statistics
Conditional
PDF on an
Event
Conditional
PDF
Total
Expectation
Theorem
CDF: Revisited
Multiple
Continuous
Random
Variables
Conditional
PDF on a
Random
Variable
5/25
Conditional PDF on an Event
Definition
A random variable
X
is called
continuous
if there is a PDF
f
X
such that
P
(
X
∈
B
) =
Z
B
f
X
(
x
)
dx
Conditional PDF
The
conditional PDF
of
X
, given an
event
A
with
P
(
A
)
>
0
,
is defined by
P
(
X
∈
B

A
) =
Z
B
f
X

A
(
x
)
dx
Probability &
Statistics
Conditional
PDF on an
Event
Conditional
PDF
Total
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 Fall '14
 LuisDavidGarciaPuente
 Probability theory, CDF, random variable X, value Y