For each problem, say if the given statement is True or False.
Give a short justification...
For each problem, say if the given statement is True or False.
Give a short justification if needed.
Let f : R + → R + be a function from the positive real numbers
to the positive real numbers, such that f(x) = x for all positive
irrational x, and f(x) = 2x for all positive rational x.
a) f is surjective (i.e. f is onto).
b) f is injective (i.e. f is one-to-one).
c) f is a bijection.
Write the R statements and associated output to compute the
following quantities. Draw a graph of...
Write the R statements and associated output to compute the
following quantities. Draw a graph of the probability mass function
or probability density function illustrating the quantity being
computed.
(a) The 90th percentile of a U(0, 20) random variable.
(b) The 20th percentile of a N(0,1) random variable.
(c) The interquartile range of a N(5, 9) random variable.
(d) The interquartile range of a binomial(10, 0.4) random
variable.
Let A = {1, 2, 3, 4, 5, 6}. In each of the following, give an...
Let A = {1, 2, 3, 4, 5, 6}. In each of the following, give an
example of a function f: A -> A with the indicated properties,
or explain why no such function exists.
(a) f is bijective, but is not the identity function f(x) =
x.
(b) f is neither one-to-one nor onto.
(c) f is one-to-one, but not onto.
(d) f is onto, but not one-to-one.
Which of the following are degree sequences of graphs? In each
case, either draw a graph...
Which of the following are degree sequences of graphs? In each
case, either draw a graph with the given degree sequence or explain
why no such graph exists.
a- (2,0,6,4,0,0,0,...)
b- (0,10,0,1,2,1,0,...)
c- (3,1,0,2,1,0,0,...)
d- (0,0,2,2,1,0,0,..)
For the following exercises, draw a graph that satisfies the
given specifications for the domain x=[−3,3]....
For the following exercises, draw a graph that satisfies the
given specifications for the domain x=[−3,3]. The function does not
have to be continuous or differentiable.
216.
f(x)>0,f′(x)>0 over x>1,−3<x<0,f′(x)=0 over
0<x<1
217.
f′(x)>0 over x>2,−3<x<−1,f′(x)<0 over
−1<x<2,f″(x)<0 for all x
218.
f″(x)<0 over
−1<x<1,f″(x)>0,−3<x<−1,1<x<3, local maximum at
x=0, local minima at x=±2
219.
There is a local maximum at x=2, local minimum at x=1, and the
graph is neither concave up nor concave down.