Question

In cycle notation,let σ=(135)(26)and τ=(456)inS6. (a) Find σ−1. (b) What is σ(3) equal to? (c) What is the order of σ? (d) Write down (in cycle notation) the elements of the cyclic subgroup of S6 generated by σ. (e) Compute στσ−1.

Answer #1

Compute the indicated operation involving the following
permutations in S6: δ = ( 1 2 3 4 5 6 3 1 4 5 6 2 ) σ =
( 1 2 3 4 5 6 2 4 5 1 6 3 ) µ = ( 1 2 3 4 5 6 5 2 4 3 1 6 )
a. δ2σ-2
b. µ23
c. Find the order of µ, |〈µ〉|.
d. Write σ as product of disjoint cycles, and as product...

A subset of a power set.
(a)
Let X = {a, b, c, d}. What is { A: A ∈ P(X) and |A| = 2 }?
comment: Please give a clear explanation to what this
set builder notation translate to? Because I've checked the answer
for a) and it is A= {{a,b}, {a,c}, {a,d}, {b,c}, {b,d},
{c,d}}.
I don't understand because the
cardinality of A has to be 2 right? Meanwhile, the answer is
basically saying there's 6 elements. So...

Let P[A] = P[B] = 1/3 and P[A ∩ B] = 1/10.
Find the following:
(a) P[A ∪ Bc ]
(b) P[Ac ∩ B]
(c) P[Ac ∪ Bc ]
Now, let P[A] = 0.38 and P[A ∪ B] = 0.84.
(d) For what value of P[B] are A and B mutually exclusive?
(e) For what value of P[B] are A and B independent?

Let lst1 = '(a b c d e),
lst2 = '(1 2 3 4 5). The
proc function takes a list as input and
returns the middle element of the list. What will be the following
expression evaluate to:
(append (cons (first lst1) '())
(cons (cdddr lst1) '())
(cons (proc lst1) '())
(cons (proc lst2) '())
(cons (fifth lst1) '())
)
a.
'(a d e c 3 e)
b.
'(a d e c 3 d)
c.
'(a (d e)...

Suppose thatA∼N(μ= 3,σ= 5),B∼N(μ= 2,σ= 4), andC∼Exp(λ= 1/6)
areindependent RVs. Find the distribution (shape, center, spread)
of the following RV expressions and state whether the distribution
is exactly or approximately equal to your claim.
1.D=A+B
2.E= 3A−2B
3.F=A1+A2+···+A14, whereA1,...,A14are independent values
fromA.
4.G=C1+C2+···+C47, whereC1,...,C47are independent values
fromC.

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?

2. For the production function ?(?, ?) = 10 ?^(1/3) ?^(1/ 3)
A)Write down the Lagrangian for the cost minimization
problem
B)Find the first-order conditions for the cost minimization
problem and e what they mean (economic terms, not math).
C). Find the contingent input demand functions. Give an
intuitive explain what they are.
D). Find the firm supply function for a firm that is a price
taker. Give an intuitive explanation of what it is.
d. Find the firm supply...

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 f(x)=(1/2)(x/5), x=1,2,3,4 Hint: Calculate F(X).
Find; (a) P(X=2) , (b) P(X≤3) , (c) P(X>2.5), (d) P(X≥1), (e)
mean and variance, (f) Graph F(x)

1)If f(x)=2x-2 and g(x)=3x+9, find the following. a)
f(g(x))=? b) g(f(x))=? c) f(f(x))=?
2)Let f(x)=x^2 and g(x)=6x-16. Find the following: a)
f(3)+g(3)=? b) f(3)*g(3)=? c) f(g(3))=? d) g(f(3))=?
3) For g(x)=x^2+3x+4, find and simplify
g(3+h)-g(3)=?
Please break down in detail. Please and Thank
you

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