In: Advanced Math

Show that the probability that all permutations of the sequence 1, 2, . . . , n have no number i being still in the ith position is less than 0.37 if n is large enough. Show all your work.

Problems 1 and 2, draw the appropriate probability
distribution curve and label all values. Show all your work. Do not
use Excel or a statistical calculator to compute the probabilities.
Showing only the answer will result in a zero grade.
Whitney Gourmet Cat Food has determined the weight of their cat
food can is normally distributed with a mean of 3 ounces and a
standard deviation of 0.05 ounces. To meet legal and customer
satisfaction goals each can must weigh...

a. Show that for all values of ? there is an infinite sequence
of positive eigenvalues of the problem
? ′′(?) + ??(?) = 0
? ?(0) + ? ′ (0) = 0, ?(1) = 0 (? = ?????)
b. Find eigenvalues of the problem if ? = 1.

Let (sn) be a sequence that converges.
(a) Show that if sn ≥ a for all but finitely many n,
then lim sn ≥ a.
(b) Show that if sn ≤ b for all but finitely many n,
then lim sn ≤ b.
(c) Conclude that if all but finitely many sn belong to [a,b],
then lim sn belongs to [a, b].

Find the number of r-permutations of the multiset
{∞?1, ∞?2, … , ∞??} such that in
every such permutation each type of an element of the multiset
appears at least
once. (You do not need to provide a short answer. Assume r ≥
n.)

Consider the sequence: x0=1/6 and xn+1 =
2xn- 3xn2 | for all natural
numbers n.
Show:
a) xn< 1/3 for all n.
b) xn>0 for all n.
Hint. Use induction.
c) show xn isincreasing.
d) calculate the limit.

If all permutations of the letters of the word "BEFORE" are
arranged in the order as in a dictionary. What is the 32 word?

The transmitter transmits either an infinite sequence of 0s with
a probability 2/3 or 1s with a probability 1/3. Each symbol,
regardless of the others and the transmitted sequence is identified
by the receiving device with an error with a probability 0.25. i)
Given that the first 5 identified symbols are 0s, find the
probability P (000000 | 00000) that the sixth received symbol is
also zero. b) Find the average value of a random variable equal to
the number...

Among all the possible permutations that can be made by all the
characters from the series of words "COMPUTER", how many different
ways that always and only three characters are in between 'P' and
'R''? Show both your work and the exact number.

Sequence 1:
5'ACTGTCGATGCTAGCTTGATCCAAGTATTGCTAGACAGAATTGACATATAGGCGATGCTAGT3'
Sequence 2:
5'ATCGCTAGGATCGCTAGATTTAAGTCGCTGATCGGCTAGATATAACAGGTCCTGAATCGCTA3'
Design a splint oligomer and write the all-possible content(s)
needed for reaction to occur.

Please solve questions 1 and 2. Please show all work and all
steps.
1.) Find the solution xa of the Bessel equation
t2x'' + tx' + t2x = 0 such that
xa(0) = a
2.) Find the solution xa of the Bessel equation
t2x'' + tx' + (t2-1)x = 0 such that
x'a(0) = a

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