Question
In: Statistics and Probability
2. Numerical “Proof” that for X,Y independent,Var(X+Y) = Var(X−Y) =σ2X+σ2Y: 2.1 As we did in Lab...
2. Numerical “Proof” that for X,Y independent,Var(X+Y) = Var(X−Y) =σ2X+σ2Y:
2.1 As we did in Lab 4, you will need to generate a sample(x,y)-values by independently generating x-values and y-values.(You may choose sample size of 50000.) State the two distributions you will use for generating x-values and y-values,and the corresponding population variances.
2.2 Compute the sample variances of the (X+Y)-values, and of the (X−Y)-values. What value are these two sample variances supposed to estimate?
2.3 Use the formula that explains the difference between the two sample variances and recompute them using the sample variances of the x- and y-values and their covariance.
please include r code
Solutions
orchestra answered 1 year agoRelated Solutions
Numerical proof of Var(X + Y ) = σ 2 X + σ 2 Y +...
Numerical proof of Var(X + Y ) = σ 2 X + σ 2 Y + 2Cov(X, Y
):
***Please use R commands, that is where my confusion lies***
2.1 State how you create a dependent pair of variables (X, Y),
give Var(X), Var(Y ), Cov(X, Y ), and Var(X + Y ).
2.2 Choose a sample size n and generate (xi , yi), i = 1, . . .
, n according to the (X,Y) distribution. Give the sample...
E(Y) = 4, E(X) = E(Y+2), Var(X) = 5, Var(Y) = Var(2X+2) a. What is E(2X...
E(Y) = 4, E(X) = E(Y+2), Var(X) = 5, Var(Y) = Var(2X+2)
a. What is E(2X -2Y)?
b. What is Var(2X-Y+2)?
c. What is SD(3Y-3X)?
2)
In a large community, 65% of the residents want to host an
autumn community fair.
The rest of the residents answer either disagree or no opinion
on this proposal.
A sample of 18 residents was randomly chosen and asked for their
opinions.
a) What is th probability that the residents answer either
disagree or...
Given: E[x] = 4, E[y] = 6, Var(x) = 2, Var(y) = 1, and cov(x,y) =...
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.
If Var(X) = 1, Var(Y) = 2 and Cov(X,Y) = 0, what is Cov(X-2Y, Y-X2)?
If Var(X) = 1, Var(Y) = 2 and Cov(X,Y) = 0, what is Cov(X-2Y,
Y-X2)?
Show that Var(x-a/)=1/h^2 Var(x)
Show
that Var(x-a/)=1/h^2 Var(x)
Proof read lab report on theory of column chromatography. We just did TLC last week and...
Proof read lab report on theory of column chromatography. We
just did TLC last week and now we are doing column.
Some key points in my background need to
include.
Describe Column chromatography and its applications
Choosing solvents for column chromatography
sample and column size
packing column two methods, adding sample, eluting column, and
monitoring column
Column chromatography is used to purify individual chemical
compounds from mixtures. Generally, it is used in a glass tube from
5 mm to 50...
Proof read lab report on theory of column chromatography. We just did TLC last week and...
Proof read lab report on theory of column chromatography. We
just did TLC last week and now we are doing column.
Some key points in my background need to
include.
Describe Column chromatography and its applications
Choosing solvents for column chromatography
sample and column size
packing column two methods, adding sample, eluting column, and
monitoring column
Column chromatography is used to purify individual chemical
compounds from mixtures. Generally, it is used in a glass tube from
5 mm to 50...
Let X and Y have the joint pdf f(x,y)=(3/2)x^2 (1-|y|) , -1<x<1, -1<y<1. Calculate Var(X). Calculate...
Let X and Y have the joint pdf f(x,y)=(3/2)x^2 (1-|y|) ,
-1<x<1, -1<y<1.
Calculate Var(X).
Calculate Var(Y).
P(−X≤Y).
Suppose X and Y are independent random variables with Exp(θ = 2) distribution. Note that, we...
Suppose X and Y are independent random variables with Exp(θ = 2)
distribution. Note that, we say X ∼ Exp(θ) if its pdf is f(x) = 1/θ
e^(−x/θ) , for x > 0 and θ > 0.
(a) What is the joint probability density function (pdf) of (X,
Y )?
(b) Use the change of variable technique (transformation
technique) to evaluate the joint pdf fW,Z (w, z) of (W, Z), where W
= X −Y and Z = Y ....
Suppose we have the following data on variable X (independent) and variable Y (dependent): X Y...
Suppose we have the following data on variable X (independent)
and variable Y (dependent):
X
Y
2
70
0
70
4
130
a.) By hand, determine the simple regression equation relating Y
and X.
b.) Calculate the R-Square measure and interpret the result.
c.) Calculate the adjusted R-Square.
d.) Test to see whether X and Y are significantly related using
a test on the population correlation. Test this at the 0.05
level.
e.) Test to see whether X and Y...
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