Prob. & Stat. Lecture06 - continuous probability distribution
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6-1
1036: Probability &
Statistics
1036: Probability &
1036: Probability &
Statistics
Statistics
Lecture 6
Lecture 6
–
–
Some Continuous
Some Continuous
Probability Distributions
Probability Distributions

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Prob. & Stat. Lecture06 - continuous probability distribution
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6-2
Continuous Uniform Distribution
•
A flat density function defined on a closed
interval.
•
The density function of continuous uniform
random variable
X
on the interval
[
A
,
B
]
is
elsewhere
,
0
,
1
)
,
;
(
B
x
A
A
B
B
A
x
f
≤
≤
⎪
⎩
⎪
⎨
⎧
−
=
Mean:
Variance:
(
)
2
B
A
+
=
µ
(
)
12
2
2
A
B
−
=
σ
Constant weight
Proof.
…

Prob. & Stat. Lecture06 - continuous probability distribution
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6-3
Normal (Gaussian) Distribution
•
The density function of the normal random
variable
X
, with mean
µ
& variance
σ
2
, is
(
)
.
,
2
exp
2
1
)
,
;
(
2
2
∞
<
<
∞
−
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−
−
=
x
x
x
n
σ
µ
π
σ
σ
µ
A function depends on
µ
and
σ
Mean:
µ
Variance:
σ
2
Proof.
…

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Prob. & Stat. Lecture06 - continuous probability distribution
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6-4
Remarks
Normal curve is dependent
on the mean and standard
deviation
…