A weighted Gauss quadrature formula for the weight function
is 
(a) The formula is exact for 
, what is 
?
(b) Use this formula to approximate the integral (keep 9 decimal places)
.
(c) Compute the error. (Note: The error is less than 
.)
Homework Answers
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A weighted Gauss quadrature formula for the weight function
is
(a) The formula is exact for...
Question 1 (Quadrature) [50 pts I. Recall the formula for a (composite) trapezoidal rule T, (u) for 1 = u(a)dr whic...
Question 1 (Quadrature) [50 pts I. Recall the formula for a (composite) trapezoidal rule T, (u) for 1 = u(a)dr which requires n function evaluations at equidistant quadrature points and where the first and the last quadrature points coincide with the integration bounds a and b, respectively. 10pts 2. For a given v(r) with r E [0,1] do a variable transformation g() af + β such that g(-1)-0 and g(1)-1. Use this to transform the integral に1, u(z)dz to an...
Use de Moivre's formula to evaluate the power (cos2+i sin2)-1 in Cartesian form. Of these multiple...
Use de Moivre's formula to evaluate the power
(cos2+i sin2)-1 in Cartesian form.
Of these multiple choice, which is correct?
A.) cos 2 - i sin 2
B.)
C.)
D.)
E.) cos 2 + i sin 2
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Negative binomial probability function: is the mean is the dispersion parameter Let there be two groups...
Negative binomial probability function:
is the mean
is the dispersion
parameter
Let there be two groups with numbers and means of
1) Write down the log-likelihood for the full model
2) Calculate the likelihood equations and find the general form
of the MLE for and
3) Write down the likelihood function in the reduced model (ie.
assuming )
and derive the MLE for in general
terms
4) Using the above answers only, give the MLE and standard error
for where...
Setup the necessary intervals to find the average value of the function over the ellipse . Use...
Setup the necessary intervals to find the average value of the
function
over the ellipse .
Use technology to evaluate the integral. Give an exact answer. (not
decimal)
We were unable to transcribe this imageWe were unable to transcribe this image
Let X(t) = 2; if 0 t 1; 3; if 1 t 3; -5; if 3 t 4: or in one formula X(t) = 2I[0;1](t) + 3I...
Let X(t) =
2; if 0 t 1;
3; if 1 t 3;
-5; if 3 t 4:
or in one formula X(t) = 2I[0;1](t) +
3I(1;3](t) -
5I(3;4](t).
Give the Itˆo integral
X(t)dB(t)
as a sum of random variables, give its distribution,
specify the mean and the variance.
We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe...
Question 4. Suppose for i=1,...,n both the mean and variance are unknown. Based on n=100 sample...
Question 4. Suppose for i=1,...,n both the mean and variance are unknown. Based on n=100 sample data, we would like to test vs a) at a type 1 error level , find a sample statistic T and the rejection region R that correctly controls exactly, i.e., find T and R that satisfy (must be exact in distribution not approximate). b) Compute the asymptotic power of T, i.e., what does converge to as sample size goes to infinity? Question 5. Following...
Can I get a solution for this question? It's quite hard to solve. There is no reference about and I don't get w...
Can I get a solution for this question? It's quite hard to solve. There is no reference about and I don't get what this question's purpose is. Is alpha the alpha from bernoulli's equation? Question: An approximate equation for the velocity distribution in a pipe with turbulent flow is where Vmax is the centerline velocity, is the distance from the wall of the pipe, r is the radius of the pipe, and n is an exponent that depends on the...
1. The Fourier series expansion of the function f(x) which is defined over one period by 3_ z, f(z) = 쓸 +Σ1@n cos...
1. The Fourier series expansion of the function f(x) which is defined over one period by 3_ z, f(z) = 쓸 +Σ1@n cos nπχ +h,sin ηπΖ] is 1<zc2. Find the coefficients an r sin ax cosar x cos ar dr = We were unable to transcribe this image
1. The Fourier series expansion of the function f(x) which is defined over one period by 3_ z, f(z) = 쓸 +Σ1@n cos nπχ +h,sin ηπΖ] is 1
Suppose that you are told that the weight of a vehicle in pounds (X) and the fuel consumption in miles per gallon(Y) are linearly related according to the model Where represents the measurement erro...
Suppose that you are told that the weight of a vehicle in pounds (X) and the fuel consumption in miles per gallon(Y) are linearly related according to the model Where represents the measurement error. X Y 3985 24 3225 27 2300 37 2500 34 2780 31 NOTE: The prediction equation is also, it is given that MSE=2.262 and a). Predict the fuel consumption for a vehicle weighing 3000 pounds b). Compute a 95% confidence interval for the fuel consumption for...
I have the answer to number 3, but need help on 4 and 5. I will up-vote. The way we approximate things, we make sure things are evenly spaced. Shifting things left and right doesn't af...
I have the answer to number 3, but need help on 4 and 5. I
will up-vote.
The way we approximate things, we make sure things are evenly spaced. Shifting things left and right doesn't affect an integral, since it's an area We will worry about horizontal scaling at the end. So let's assume (without loss of generality) that the r values of our coordinates are 0,1,2, and 3. We will write our points as (0, fo), (1, fi), (2,...
Question 1 (Quadrature) [50 pts I. Recall the formula for a (composite) trapezoidal rule T, (u) for 1 = u(a)dr which requires n function evaluations at equidistant quadrature points and where the first and the last quadrature points coincide with the integration bounds a and b, respectively. 10pts 2. For a given v(r) with r E [0,1] do a variable transformation g() af + β such that g(-1)-0 and g(1)-1. Use this to transform the integral に1, u(z)dz to an...
Use de Moivre's formula to evaluate the power
(cos2+i sin2)-1 in Cartesian form.
Of these multiple choice, which is correct?
A.) cos 2 - i sin 2
B.)
C.)
D.)
E.) cos 2 + i sin 2
We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
Negative binomial probability function:
is the mean
is the dispersion
parameter
Let there be two groups with numbers and means of
1) Write down the log-likelihood for the full model
2) Calculate the likelihood equations and find the general form
of the MLE for and
3) Write down the likelihood function in the reduced model (ie.
assuming )
and derive the MLE for in general
terms
4) Using the above answers only, give the MLE and standard error
for where...
Setup the necessary intervals to find the average value of the
function
over the ellipse .
Use technology to evaluate the integral. Give an exact answer. (not
decimal)
We were unable to transcribe this imageWe were unable to transcribe this image
Let X(t) =
2; if 0 t 1;
3; if 1 t 3;
-5; if 3 t 4:
or in one formula X(t) = 2I[0;1](t) +
3I(1;3](t) -
5I(3;4](t).
Give the Itˆo integral
X(t)dB(t)
as a sum of random variables, give its distribution,
specify the mean and the variance.
We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe...
1. The Fourier series expansion of the function f(x) which is defined over one period by 3_ z, f(z) = 쓸 +Σ1@n cos nπχ +h,sin ηπΖ] is 1<zc2. Find the coefficients an r sin ax cosar x cos ar dr = We were unable to transcribe this image
1. The Fourier series expansion of the function f(x) which is defined over one period by 3_ z, f(z) = 쓸 +Σ1@n cos nπχ +h,sin ηπΖ] is 1
I have the answer to number 3, but need help on 4 and 5. I
will up-vote.
The way we approximate things, we make sure things are evenly spaced. Shifting things left and right doesn't affect an integral, since it's an area We will worry about horizontal scaling at the end. So let's assume (without loss of generality) that the r values of our coordinates are 0,1,2, and 3. We will write our points as (0, fo), (1, fi), (2,...
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