Let S be a sample space and E and F be events associated with S . Suppose that Pr ( E ) = .6 , Pr ( F ) = .3 , and Pr ( E ∩ F ) = .2 . Calculate a. Pr ( E | F ) b. Pr ( F | E ) c. Pr ( E | F ′ ) d. Pr ( E ′ | F ′ ) .
Let S be a sample space and E and F be events associated with S . Suppose that Pr ( E ) = .6 , Pr ( F ) = .3 , and Pr ( E ∩ F ) = .2 . Calculate a. Pr ( E | F ) b. Pr ( F | E ) c. Pr ( E | F ′ ) d. Pr ( E ′ | F ′ ) .
Solution Summary: The author calculates the value of Pr(E|F) if the sample space is S and the events are E and F.
Let S be a sample space and E and F be events associated with S. Suppose that
Pr
(
E
)
=
.6
,
Pr
(
F
)
=
.3
,
and
Pr
(
E
∩
F
)
=
.2
. Calculate
a.
Pr
(
E
|
F
)
b.
Pr
(
F
|
E
)
c.
Pr
(
E
|
F
′
)
d.
Pr
(
E
′
|
F
′
)
.
Definition Definition For any random event or experiment, the set that is formed with all the possible outcomes is called a sample space. When any random event takes place that has multiple outcomes, the possible outcomes are grouped together in a set. The sample space can be anything, from a set of vectors to real numbers.
Let T be a tree. Prove that if T has a vertex of degree k, then T has at least k leaves.
Homework Let X1, X2, Xn be a random sample from f(x;0) where
f(x; 0) = (-), 0 < x < ∞,0 € R
Using Basu's theorem, show that Y = min{X} and Z =Σ(XY) are indep.
-
Homework Let X1, X2, Xn be a random sample from f(x; 0) where
f(x; 0) = e−(2-0), 0 < x < ∞,0 € R
Using Basu's theorem, show that Y = min{X} and Z =Σ(XY) are indep.
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