Sharpening Your Skills In Exercises 21 – 26 , find, if possible, the number of elements in sets A , B , and C using the given information. If there is an inconsistency in the information, state where it occurs. A ∩ C = ∅ , n ( A ∩ B ) = 3 , n ( C − B ) = 2 , n ( B − C ) = 7 , n ( B ∪ C ) = 16 , n ( A ∪ B ) = 16.
Sharpening Your Skills In Exercises 21 – 26 , find, if possible, the number of elements in sets A , B , and C using the given information. If there is an inconsistency in the information, state where it occurs. A ∩ C = ∅ , n ( A ∩ B ) = 3 , n ( C − B ) = 2 , n ( B − C ) = 7 , n ( B ∪ C ) = 16 , n ( A ∪ B ) = 16.
Solution Summary: The author explains how to find the number of elements in A,B and C, using the given information.
In Exercises 21 –26, find, if possible, the number of elements in sets
A
,
B
, and
C
using the given information. If there is an inconsistency in the information, state where it occurs.
A
∩
C
=
∅
,
n
(
A
∩
B
)
=
3
,
n
(
C
−
B
)
=
2
,
n
(
B
−
C
)
=
7
,
n
(
B
∪
C
)
=
16
,
n
(
A
∪
B
)
=
16.
28. (a) Under what conditions do we say that two random variables X and Y are
independent?
(b) Demonstrate that if X and Y are independent, then it follows that E(XY) =
E(X)E(Y);
(e) Show by a counter example that the converse of (ii) is not necessarily true.
7. [10 marks]
Let G = (V,E) be a 3-connected graph with at least 6 vertices. Let C be a cycle in G
of length 5. We show how to find a longer cycle in G.
(a) Let x be a vertex of G that is not on C. Show that there are three C-paths
Po, P1, P2 that are disjoint except at the shared initial vertex and only intersect
C at their final vertices.
(b) Show that at least two of P0, P1, P2 have final vertices that are adjacent along C.
(c) Combine two of Po, P1, P2 with C to produce a cycle in G that is longer than C.
1. Let X and Y be random variables and suppose that A = F. Prove that
Z XI(A)+YI(A) is a random variable.
Elementary Statistics Using The Ti-83/84 Plus Calculator, Books A La Carte Edition (5th Edition)
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