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?
1) Suppose that X and Y are two random variables, which may be
dependent and Var(X)=Var(Y)....
1) Suppose that X and Y are two random variables, which may be
dependent and Var(X)=Var(Y). Assume that 0<Var(X+Y)<∞ and
0<Var(X-Y)<∞. Which of the following statements are NOT true?
(There may be more than one correct answer)
a. E(XY) = E(X)E(Y)
b. E(X/Y) = E(X)/E(Y)
c. (X+Y) and (X-Y) are correlated
d. (X+Y) and (X-Y) are not correlated.
2) S.D(X ± Y) is equal to, where S.D means standard
deviation
a. S.D(X) ± S.D(Y)
b. Var(X) ± Var(Y)
c. Square...
Let X and Y be jointly distributed random variables with means,
E(X) = 1, E(Y) =...
Let X and Y be jointly distributed random variables with means,
E(X) = 1, E(Y) = 0, variances, Var(X) = 4, Var(Y ) = 5, and
covariance, Cov(X, Y ) = 2.
Let U = 3X-Y +2 and W = 2X + Y . Obtain the following
expectations:
A.) Var(U):
B.) Var(W):
C. Cov(U,W):
ans should be 29, 29, 21 but I need help showing how to
solve.
5. Let X1, X2, . . . be independent random variables all with
mean E(Xi) =...
5. Let X1, X2, . . . be independent random variables all with
mean E(Xi) = 7 and variance
Var(Xi) = 9. Set
Yn =
X1 + X2 + · · · + Xn
n
(n = 1, 2, 3, . . .)
(a) Find E(Y2) and E(Y5).
(b) Find Cov(Y2, Y5).
(c) Find E (Y2 | X1).
(d) How should your answers from parts (a)–(c) be modified if the
numbers “2”, “5”, “7” and
“9” are replaced by m,...
1. Let D={0,1,2,3,4,5,6,7,8,9} be the set of digits. Let P(D) be
the power set of D,...
1. Let D={0,1,2,3,4,5,6,7,8,9} be the set of digits. Let P(D) be
the power set of D, i.e. the set of all subsets of D.
a) How many elements are there in P(D)? Prove
it!
b) Which number is greater: the number of different
subsets of D which contain the digit 7 or the number of different
subsets of D which do not contain the digit 7? Explain why!
c) Which number is greater: the number of different...
True or false; for each of the statements below, state whether
they are true or false....
True or false; for each of the statements below, state whether
they are true or false. If false, give an explanation or example
that illustrates why it's false.
(a) The matrix A = [1 0] is not invertible.
[1 -2]
(b) Let B be a matrix. The rowspaces row (B), row (REF(B)) and
row (RREF(B)) are all equivalent.
(c) Let C be a 5 x 7 matrix with nullity 3. The rank of C is
2.
(d) Let D...
1) Let A = {1, 2, · · · , 10} and B = {1,2,3, a,...
1) Let A = {1, 2, · · · , 10} and B = {1,2,3, a, b, c, d}
then |A ∩B|=
2) How many 8 digit telephone numbers can be made from {0, 1, 2,
3, 4, 5, 6, 7, 8, 9} such that the first digit is not 0?
(Repetition of a digit is allowed.)
3) Let A = {1, 2, · · · , 10} and B = {1,2,3, a, b, c, d}
then |A − B|=
4) Let A =...