Question

- If the solution of a difference equation is
*y**n**=-15.625+18.425**(3.4)**n*, then determine the difference equation (with initial value). Show the steps needed to arrive at the answer.

Answer #1

Prove that for a sample of n where Xi ~ iid Bernoulli
(p) and Yn = ∑Xi, that
Bn
= [Yn
– np] / √[np(1-p)] -->D N(0,1)
i.e. Bn has a limiting distribution of the standard
normal. No need to use the MGF, you can use a theorem to answer
this (which you must identify). Show all steps and parameterize the
RV as the theorem specifies

A Bernoulli differential equation is one of the form
dxdy+P(x)y=Q(x)yn
Observe that, if n=0 or 1, the Bernoulli equation is linear. For
other values of n, the substitution u=y^(1−n) transforms the
Bernoulli equation into the linear equation
du/dx+(1−n)P(x)u=(1−n)Q(x)
Use an appropriate substitution to solve the equation
y'−(3/x)y=y^4/x^2 and find the solution that satisfies y(1)=1

Let X1, X2, ..., Xn be a random sample (of size n) from U(0,θ).
Let Yn be the maximum of X1, X2, ..., Xn.
(a) Give the pdf of Yn.
(b) Find the mean of Yn.
(c) One estimator of θ that has been proposed is Yn. You may
note from your answer to part (b) that Yn is a biased estimator of
θ. However, cYn is unbiased for some constant c. Determine c.
(d) Find the variance of cYn,...

A
rule of thumb states that cars used for personal use depreciates by
15% each year (that is the value of the car is 15% less at the end
of the year as it was at the beginning of the year). Suppose that a
new car is purchased for $30,000. Let Yn be the value of the car
after n years. Do the following:
(a) Create the difference equation that will model the cars
value.
(b) Solve the difference equation....

dy/dt - 2y = 7e^(2t)
a. Determine the general solution to the associated homogeneous
equation.
b. By choosing an appropriate guess, determine a particular
solution to this differential equation.
c. Using your answers from parts (a) and (b), write down the
general solution to the original equation
d. Check that your solution is correct by plugging it into the
original ODE.
e. Determine the specific solution corresponding to the initial
condition y(0)= 3
Pls explain how you did it

7. Determine
the first 4 nonzero terms of the Taylor series for the solution
y = φ(x) of the given initial value
problem, y’’ +
cos(x)y’ +
x2y = 0; y(0) = 1,
y’(0) = 1.
What do you expect the radius of convergence to be? Why?
please show all steps

Determine each of the following for a 0.063 M KOH solution.
Determine [H3O+] for this solution? PH? Write a balanced equation
for the reaction with H2SO4. Express answer as a chemical equation.
Also calculate the volume in milliliter of KOH solution required to
neutralize 33.0 mL of a 0.043 MH2SO4 solution

If a buffer solution is 0.160 M in a weak acid (Ka = 3.4 × 10-5)
and 0.510 M in its conjugate base, what is the pH? If a buffer
solution is 0.260 M in a weak base (Kb = 6.9 × 10-5) and 0.550 M in
its conjugate acid, what is the pH?
Please show work that way it's actually learning and not just
giving an answer. Thank you!

(Linear Algebra) Consider the difference equation.
yk+2 - 4yk+1 + 4yk = 0, for all
k
(a) After using auxiliary equation, the solutions have the form
rk and k(rk). Find the root, r, and show that
yk = k(rk) is a solution.
(b) Show that rk and k(rk) are linearly
independent and form the general solution of the difference
equation.

For the below ordinary differential equation with initial
conditions, state the order and determine if the equation is linear
or nonlinear. Then find the solution of the ordinary differential
equation, and apply the initial conditions. Verify your solution.
x^2/(y^2-1) dy/dx=(3x^3)/y, y(0)=2

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