Let the population have N=7 units, with {(unit,value)} =
{(A,-1),(B,+1),(C,-2),(D,+3),(E,-4),(F,+5),(G,-6)}. The design is
as follows: first...
Let the population have N=7 units, with {(unit,value)} =
{(A,-1),(B,+1),(C,-2),(D,+3),(E,-4),(F,+5),(G,-6)}. The design is
as follows: first choose A or B at random; if A then choose from
{C,D} at random, if B then choose from {E,F,G} at random. 1) Find
the first-order inclusion probabilities (note that the sample size
n is fixed at 2).
Verify (show numerically for this example) that the
Horvitz-Thompson estimator is unbiased for the population total.
(Hint: find the probability of each sample and the value...
Let X = {1, 2, 3} and Y = {a, b, c, d, e}.
(1) How...
Let X = {1, 2, 3} and Y = {a, b, c, d, e}.
(1) How many functions f : X → Y are there?
(2) How many injective functions f : X → Y are there?
(3) What is a if (x + 2)10 = x 10 + · · · + ax7 + · · · + 512x +
1024?
Consider the following symbols and their frequencies: a:1, b:2,
c:3, d:4, e:5, f:6
What is the...
Consider the following symbols and their frequencies: a:1, b:2,
c:3, d:4, e:5, f:6
What is the amount of bits needed per character for a balanced
tree encoding.
If the matrix A is 4×2, B is 3×4, C is 2×4, D is 4×3,
and...
If the matrix A is 4×2, B is 3×4, C is 2×4, D is 4×3,
and E is 2×5, what are the
dimensions of the following expressions
a) A^TD + CB^T
b) (B + D^T ) A
c) CA + CB^T
1. Let T = {(1, 2), (1, 3), (2, 5), (3, 6), (4, 7)}. T :...
1. Let T = {(1, 2), (1, 3), (2, 5), (3, 6), (4, 7)}. T : X ->
Y. X = {1, 2, 3, 4}, Y = {1, 2, 3, 4, 5, 6, 7}
a) Explain why T is or is not a function.
b) What is the domain of T?
c) What is the range of T?
d) Explain why T is or is not one-to one?
Define variables as follows: a = 1; b= 2; c = 3; d = 4; e...
Define variables as follows: a = 1; b= 2; c = 3; d = 4; e = 5; f
= 6; g = 7; h = 8; i = 9; j =10; Using Matlab operations (no
hard-coding), perform the following operations (in order): 1a) Add
one to the value of a, and store the result in a 1b) Cube b, add
the value of c to this, and store the result in b 1c) Set c equal
to the larger...
a = [-5, -3, 2] b = [1, -7, 9] c = [7, -2, -3] d...
a = [-5, -3, 2] b = [1, -7, 9] c = [7, -2, -3] d = [4, -1, -9,
-3] e = [-2, -7, 5, -3]
a. Find (d) (e)
b. Find (3a) (7c)
c. Find Pe --> d
d. Find Pc --> a +2b
ex. C = |x|(xy/xy) C = xy/|x|
ex. P x --> y = Cux = C(xy/x) (1/|x|) (x) =( xy/yy)(y)
Let Let A = {a, e, g} and B = {c, d, e, f, g}. Let...
Let Let A = {a, e, g} and B = {c, d, e, f, g}. Let f : A → B and
g : B → A be defined as follows: f = {(a, c), (e, e), (g, d)} g =
{(c, a), (d, e), (e, e), (f, a), (g, g)}
(a) Consider the composed function g ◦ f.
(i) What is the domain of g ◦ f? What is its codomain?
(ii) Find the function g ◦ f. (Find...
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.