5. Find a closed-form formula for the exponential generating
function for the number of strings of...
5. Find a closed-form formula for the exponential generating
function for the number of strings of length n with symbols a, b,
c, where (number of a′s) + (number of b′s) ≥ 1; and, # c′s =
even
5. Find the generating function for the number of ways to create
a bunch of n balloons selected from white, gold, and blue balloons
so that the bunch contains at least one white balloon, at least one
gold balloon, and at most two blue balloons. How many ways are
there to create a bunch of 10 balloons subject to these
requirements?
This is a Combinatorics question.
Find a generating function for a sub r, the number of
ways:
(1) To distribute ridentical objects into seven
distinct boxes with an odd numbet of objects not exceeding nine in
the first three boxes and between four and ten in the other
boxes.
Use
inclusion-exclusion to find the number of binary strings of length
5 that have at least one of the following characteristics: start
with a 1, end with a 0, or contain exactly two
a) Find the analytic MLE formula for exponential distribution
exp(λ). Show that MLE is the same as MoM estimator here. (b) A
random sample of size 6 from the exp(λ) distribution results in
observations: 1.636, 0.374, 0.534, 3.015, 0.932, 0.179. Find the
MLE on this data set in two ways: by numerical optimization of the
likelihood and by the analytic formula. For (b): please give both
values from the analytic MLE formula and numerical MLE solution on
this data set....
Find the closed formula solution to each of the following
recurrence relations with the given initial conditions. Use an
iterative approach and show your work! What is a_100? a)
a_n=a_(n-1)+2,a_0=3 b) a_n=a_(n-1)+2n+3,a_0=4 c)
a_n=2a_(n-1)-1,a_0=1 d) a_n=-a_(n-1),a_0=5
Find the closed formula solution to each of the following
recurrence relations with the given initial conditions. Use an
iterative approach and show your work! What is
a100 ?
an=an-1+2,
a0=3
an=an-1+2n+3,
a0=4
an=2an-1-1,
a0=1
an=-an-1,
a0=5
Find either a linear or an exponential function that models the
data in the table.
x
−3
−2
−1
0
1
y
128
64
32
16
8
f(x)=
(Use integers or fractions for any numbers in the
expression.)
Note: Please show how to solve using TI-84 Plus calculator