In: Statistics and Probability

Explain why ρ is preferable to Cov(X,Y) in measuring the strength of relationship between X and Y

ρ or the correlation coefficient is preferable because it allows comparing the magnitude and the direction of the strength of the relationship between X and Y very easily. ρ can take values between -1 and 1. Since we have a fixed scale between which ρ lies, it is easier to discern the magnitude of the linear relationship between the two variables. For example, if ρ = -1, it means that the variables are perfect negatively correlated. It increasing from -1 to 0 shows that the degree of the negative association between the two variables is becoming weaker. 0 means the absence of a linear relationship. As ρ increases from 0 to 1, the degree of the positive association between the variables increase.

since Cov(X,Y) can take any value, comparing the magnitude or strength of the relationship between X and Y is not possible. Hence ρ is preferrable.

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Identify the type of correlation coefficient apprpriate for
measuring the relationship between X and Y :
1. X= sex (M or F); Y= income (dollars)
2. X= IQ (above of below 100); Y= GPA (above or below
60%)

If Var(X) = 1, Var(Y) = 2 and Cov(X,Y) = 0, what is Cov(X-2Y,
Y-X2)?

A lamina with constant density
ρ(x, y) =
ρ
occupies the given region. Find the moments of inertia
Ix
and
Iy
and the radii of gyration and .
The part of the disk
x2 +
y2 ≤
a2
in the first quadrant

Provide an example that if the
cov(X,Y)
= 0, the two random variables, X and Y, are not necessarily
independent.
Would you please give the example specifically and
why?

Provide an example that if the
cov(X,Y)
= 0, the two random variables, X and Y, are not necessarily
independent.
Would you please give the example specifically and
why?

Regression
Is there a relationship between the number of stories a building has and its height? Some statisticians compiled data on a set of n = 60 buildings reported in the World Almanac. You will use the data set to decide whether height (in feet) can be predicted from the number of stories.
(a) Load the data from buildings.txt.(Note that this is a text file, so use the appropriate instruction. If you are having trouble uploading the data, open...

Given:
E[x] = 4, E[y] = 6, Var(x) = 2, Var(y) = 1, and cov(x,y) =
0.2
Find a lower bound on (5 < x + y < 10). State the theorem
used.

Find if there is a relationship between education (in years) X
and income Y.
x
4
6
8
11
12
14
16
17
20
y
6000
12000
14000
10000
17000
16000
13000
16000
19000
Make sure that THREE of your posts for the week are Statistical
in nature AND a direct response to the problems given in the
discussion

Calculate the covariance between variables X and Y. Is it a
positive or negative relationship between the two variables?
b. Calculate correlation coefficient between X and Y. Is it a
positive or negative relationship? Is it a strong linear, weak
linear or nonlinear relationship between X and Y?
c. Use the Y data to calculate mean, range, standard deviation
and variance.
d. Use the first Y value to calculate the Z-score. Is it an
outlier?
e. Calculate the 60th percentile...

For x = ρsinφcosθ; y = ρsinφsinθ; z = ρcosφ:
a/ Express ∂^2/∂y^2 with ρ, φ, θ, and their partials.
b/ Express ∂^2/∂z^2 with ρ, φ, θ, and their partials.
c/ Express the Laplacian operator using spherical
coordinates.

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