Question

1. Let θ < 0 be an angle in standard position. (a) Choose a value for θ (in radians) and graph θ. (b) Find the reference angle of θ. (c) Find numbers 0 < x < 2π and n ∈ Z so that θ = x + 2πn. (d) Convert θ into degrees.

2. Let θ_{1} and θ_{2} be coterminal angles in
standard position. (a) Choose a value for θ_{1} and
θ_{2} (in radians) and graph both angles. (b) Find the
reference angle of θ_{1} and θ_{2}. (c) Find
numbers 0 < x_{1} < 2π and n_{1} ∈ Z so that
θ = x_{1} + 2πn_{1}. (d) Find numbers 0 <
x_{2} < 2π and n_{2} ∈ Z so that θ =
x_{2} + 2πn_{2}.

Answer #1

1) The measure of an angle in standard position is given. Find
two positive angles and two negative angles that are coterminal
with the given angle. (Enter your answers as a comma-separated
list.)
3π
4
2) The measure of an angle in standard position is given. Find
two positive angles and two negative angles that are coterminal
with the given angle. (Enter your answers as a comma-separated
list.)
−
5π
4
3) The measure of an angle in standard position...

Find the angle θ (in radians and degrees) between the
lines. (Let 0 ≤ θ < π/2 and 0 ≤ θ
< 90°. Round your answers to three decimal places.)
0.02x
−
0.05y
=
−0.23
0.01x
+
0.04y
=
0.52

1.A circular arc of length 10 cm subtends the central angle
θ on a circle with radius 6 cm.
(a) Find the degree measure of the central angle θ. Give
your answer correct to 2 decimal places.
θ = °
(b) Find the area of the sector determined by θ. Give your
answer correct to 2 decimal places.
Area = cm2
2.The 660°angle is in standard position. Determine which of the
choices are coterminal angles. (Select all that apply)660°
570°, 1380°, 300°,...

1. Find all angles
θ,0≤θ≤2π
(Double angle
formula, To two decimal places)
a) Tan theta
= 0.3, b) cos theta = 0.1, c) sin theta = 0.1,
d) sec theta
= 3

Let X1,...,Xn be a random sample from the pdf f(x;θ) = θx^(θ−1)
, 0 ≤ x ≤ 1 , 0 < θ < ∞ Find the method of moments estimator
of θ.

Let X_1,…, X_n be a random sample from the Bernoulli
distribution, say P[X=1]=θ=1-P[X=0].
and
Cramer Rao Lower Bound of θ(1-θ)
=((1-2θ)^2 θ(1-θ))/n
Find the UMVUE of θ(1-θ) if such exists.
can you proof [part (b) ] using (Leehmann Scheffe
Theorem step by step solution) to proof
[∑X1-nXbar^2 ]/(n-1) is the umvue , I have the key
solution below
x is complete and sufficient.
S^2=∑ [X1-Xbar ]^2/(n-1) is unbiased estimator of θ(1-θ) since
the sample variance is an unbiased estimator of the...

1. Al Einstein has a utility function that we can describe by
u(x1, x2) = x21 +
2x1x2 + x22
. Al’s wife, El Einstein, has a utility function v(x1,
x2) = x2 + x1.
(a) Calculate Al’s marginal rate of substitution between
x1 and x2.
(b) What is El’s marginal rate of substitution between
x1 and x2?
(c) Do Al’s and El’s utility functions u(x1,
x2) and v(x1, x2) represent the
same preferences?
(d) Is El’s utility function a...

1. Let x be a continuous random variable. What is the
probability that x assumes a single value, such as a (use numerical
value)?
2. The following are the three main characteristics of a normal
distribution.
The total area under a normal curve equals _____.
A normal curve is ___________ about the mean. Consequently, 50%
of the total area under a normal distribution curve lies on the
left side of the mean, and 50% lies on the right side of...

R Code
Directions: All work has to be your own, you may not work in
groups. Show all work. Submit your solutions in a pdf document on
Moodle. Include your R code (which must be
commented and properly indented) in the pdf file. Name this pdf
file ‘your last name’-HW5.pdf. Also submit one text file with your
R code, which must be commented and properly indented. You may only
use ‘runif’ to generate random numbers; other random number
generating functions...

The following data represent soil water content (percentage of
water by volume) for independent random samples of soil taken from
two experimental fields growing bell peppers. Soil water content
from field I: x1; n1 = 72 15.2 11.3 10.1 10.8 16.6 8.3 9.1 12.3 9.1
14.3 10.7 16.1 10.2 15.2 8.9 9.5 9.6 11.3 14.0 11.3 15.6 11.2 13.8
9.0 8.4 8.2 12.0 13.9 11.6 16.0 9.6 11.4 8.4 8.0 14.1 10.9 13.2
13.8 14.6 10.2 11.5 13.1 14.7 12.5...

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