Show that the Legendre polynomials P1 and P2 are orthogonal by
explicit integration. Also show that...
Show that the Legendre polynomials P1 and P2 are orthogonal by
explicit integration. Also show that when (P2)^ 2 is integrated
over the full range of integration, the result is 2 /(2l+1) , where
l is the order of the polynomial.
in the book, Legendre polynomials are obtained to the
degree 5. Normalize polynomials P4 and P5 so that
P4(1) = 1 and p5(1) = 1. This is standard normalization
and these will be standard Legendre polynomials.
Use the recurrence relation for standard Legendre
polynomials
to find two more (standard) Legendre polynomials.
Show your work for credit.
Hint: The recurrence relation:
(n+1) P_{n+1}(x) = (2n+1) P_{n}(x) - n P_{n-1}(x)}
Two polynomials in the variable x are represented by the coefficient vectors p1 = [6,2,7,-3] and p2 = [10,-5,8].
a. Use MuPAD to find the product of these two polynomials; express the product in its simplest form.
b. Use MuPAD to find the numeric value of the product if x = 2.
. Consider this hypothesis test:
H0: p1 - p2 = < 0
Ha: p1 - p2 > 0
Here p1 is the population proportion of “happy” of Population
1 and p2 is the population proportion of “happy” of Population 2.
Use the statistics data from a simple random sample of each of the
two populations to complete the following:
Population 1
Population 2
Sample Size (n)
1000
1000
Number of “yes”
600
280
a. Compute the test statistic z.
b....
1. Consider this hypothesis test:
H0: p1 - p2 = < 0
Ha: p1 - p2 > 0
Here p1 is the population proportion of “happy” of Population
1 and p2 is the population proportion of “happy” of Population 2.
Use the statistics data from a simple random sample of each of the
two populations to complete the following:
Population 1
Population 2
Sample Size (n)
1000
1000
Number of “yes”
600
280
a. Compute the test statistic z.
b....
Consider this hypothesis test:
H0: p1 - p2 = 0
Ha: p1 - p2 > 0
Here p1 is the population proportion of “yes” of Population 1
and p2 is the population proportion of “yes” of Population 2. Use
the statistics data from a simple random sample of each of the two
populations to complete the following: (8 points)
Population 1 Population 2
Sample Size (n) 500 700
Number of “yes” 400 560
Compute the test statistic z.
What is...