Question

For the following generating function, provide a closed formula for the sequence it determines:

x^{2}/(1-x)^{3}

Answer #1

Find closed form expression for the generating function of the
sequence:
Sk + Sk-1 – 42Sk-2 = 0 for k ≥ 2, with S0 = 2 and S1 = 2.

What is the sequence corresponding to the generating
function:
(6 - 3z) / (1 - z - 6x2)

The random variable X has moment generating function
ϕX(t)=(0.44e^t+1−0.44)^8
Provide answers to the following to two decimal places
(a) Evaluate the natural logarithm of the moment generating
function of 3X at the point t=0.4.
(b) Hence (or otherwise) find the expectation of 3X.
(c) Evaluate the natural logarithm of the moment generating
function of 3X+6 at the point t=0.4.

What is the sequence corresponding to the generating function :
(6-3z) / (1-Z-6Z^2) ?

Poisson Distribution: p(x,
λ) = λx exp(-λ)
/x! , x = 0, 1, 2, …..
Find the moment generating function Mx(t)
Find E(X) using the moment generating function
2. If X1 , X2 ,
X3 are independent and have means 4, 9, and
3, and variencesn3, 7, and 5. Given that Y =
2X1 - 3X2 +
4X3. find the
mean of Y
variance of Y.
3. A safety engineer claims that 2 in 12 automobile accidents
are due to driver fatigue. Using the formula for Binomial
Distribution find the...

The random variable X has moment generating function
ϕX(t)=exp((9t)^2)/2)+15t)
Provide answers to the following to two decimal places
(a) Evaluate the natural logarithm of the moment generating
function of 2X at the point t=0.62.
(b) Hence (or otherwise) find the expectation of 2X.
c) Evaluate the natural logarithm of the moment generating
function of 2X+7 at the point t=0.62.

Let
h(x)=(x2+2x-3)(x2+4x+4)-1
Select one:
a. The function has a loc. max. at x=-3 and an inflection pt at
x=-1
b. The function has a horizontal asymptote y=1 and a vertical
asymptote x=-3.
c. The function has a horizontal asymptote y=1 and a vertical
asymptote x=-2.
d. The function has an abs. min. at x=-1 and is concave up on
(-∞, ∞).
e. The function has an abs. min. at x=-1 and is concave down on
(-∞, ∞)

Suppose that a random variable X has the following
moment generating function,
M X (t) = (1 −
3t)−8, t < 1/3. (a)
Find the mean of X (b) Find the Varience of X. Please explain
steps. :) Thanks!

10. Show that (1-x-x^2-x^3-x^4-x^5-x^6)^-1 is the generating
function for the number of ways a sum of r can occur if a die is
rolled any number of times

What is the generating function for the number of non-negative
integer solutions to
x1 + x2 + x3 + x4 + x5 = 50
if:
1.) There are no restrictions
2.) xi >= 2 for all i
3.) x1 <= 10
4.) xi <= 12 for all i
5.) if x1 is even

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