The bar graph shows the percentage of Americans, by age group, supporting legalized marijuana for four selected years from 1969through 2015. Use the information in the graph to write each set inExercises 133-138 in roster form or express the set as ∅ . 134. { x | x | was a year in which more than 30% of age group18-34 supported legalization} ∩ { x | x | was a year in which fewer than 14% of age group 65+supported legalization} {1985}
The bar graph shows the percentage of Americans, by age group, supporting legalized marijuana for four selected years from 1969through 2015. Use the information in the graph to write each set inExercises 133-138 in roster form or express the set as ∅ . 134. { x | x | was a year in which more than 30% of age group18-34 supported legalization} ∩ { x | x | was a year in which fewer than 14% of age group 65+supported legalization} {1985}
The bar graph shows the percentage of Americans, by age group, supporting legalized marijuana for four selected years from 1969through 2015. Use the information in the graph to write each set inExercises 133-138 in roster form or express the set as
∅
.
134.
{
x
|
x
|
was a year in which more than 30% of age group18-34 supported legalization}
∩
{
x
|
x
|
was a year in which fewer than 14% of age group 65+supported legalization} {1985}
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.
Chapter 2 Solutions
Pearson eText for Thinking Mathematically -- Instant Access (Pearson+)
University Calculus: Early Transcendentals (4th Edition)
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