In: Statistics and Probability

Suppose the proportion X of surface area in a randomly selected quadrat that is covered by a certain plant has a standard beta distribution with α = 5 and β = 3.

(a) Compute E(X) and V(X). (Round your answers to four decimal places.)

E(X) =

V(X) =

b) Compute P(X ≤ 0.6). (Round your answer to four decimal places.)

(c) Compute P(0.6 ≤ X ≤ 0.8). (Round your answer to four decimal places.)

(d) What is the expected proportion of the sampling region not covered by the plant? (Round your answer to four decimal places.)

Let X denote the proportion of allotted time that a randomly
selected student spends working on a certain aptitude test. Suppose
the pdf of X is
f(x) = {
(θ+1)x^θ, for 0≤x≤1
0, otherwise }
where −1<θ.
A random sample of ten students yields data x1=.92, x2=.79,
x3=.90, x4=.65, x5=.86, x6=.47, x7=.73, x8=.97, x9=.94,
x10=.77.
(a) Use the method of moments to obtain an estimator of θ, and
then compute the estimate for this data.
(b) Obtain the maximum likelihood...

Suppose you randomly selected 40 gas stations in the Baton Rouge
area and found that the average price of regular unleaded gas is
$3.04. Assume that population standard deviation is known to be
$0.25. Construct and interpret a 95% confidence interval for the
true mean of the gas price.

1) Suppose you have the following data, which represents the
area codes of 50 randomly selected students from endicott. Area
code: 617,508,857 other. # of students 25,10,10,5 a) is the area
code variable quantitative or categorical? Explain your reasoning.
b) Create a bar graph to represent the area code data, using
percents as the y-axis. Draw a sketch below, or attach a labeled
graph from excel to the end of this exam. Make sure to label your
graphs' axes and...

Classify the following random variables as discrete or
continous.
1) The surface area of a randomly selected person's body.
2) The quantity of oil in a randomly selected oil spill in the
sea.
3) The quantity of pots in a randomly selected restaurant
kitchen.
4) The total cent value of all the coins in a randomly selected
person's pockets.

a sample of 193 randomly selected students , found that the
proportion of students planning to travel home for thanksgiving is
0.71

Multivariable Calculus: Surface Area and Change of Variables
Find the surface area of the surface given by z
=18−2x−3y over the triangle with vertices: (0,0), (2,3), (4,1).
Since this is not a type I or type II region, you will either need
to divide the region into two regions or use a change of variables.
x=(1/5)(u-2v) and y=(1/10)(3u-v) is a possible change of
variables.
I will upvote answers!

Find the area of a surface of revolution revolving about the
x-axis.
? = 3? , 0 ≤ ? ≤ 3

The probability that a randomly selected person is left-handed
is 0.1. Suppose we are to randomly select 10 people. Let X be the
number of people selected out of the 10 that are left-handed. Find
the following probabilities:
(a) P(X = 2) =
(b) P(X ≤ 2) =
(c) P(X > 2) =

Different hotels in a certain area are randomly selected, and
their ratings and prices were obtained online. Using technology,
with x representing the ratings and y representing price, we find
that the regression equation has a slope of 125 and a y-intercept
of negative 374. Complete parts (a) and (b) below.
a. What is the equation of the regression line? Select the
correct choice below and fill in the answer boxes to complete your
choice. A. yequals nothingplusleft parenthesis nothing...

Suppose that we have a reservoir that has a surface area of 50
acres, with an average depth when full of 15 meters. [Conversion: 1
acre = 4096.86 square meters] If the reservoir were to start out
with a depth of 0 meters and eventually be filled to a depth of 15
meters, (1) how much volume of water will have been added in the
filling of the reservoir from 0 meters depth to 15 meters
depth?
(2) What mass...

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