> x=c(5,3,1,6,4,3,2,6,7)
> y=c(7,4,1,8,5,2,4,7,9)
> mean(x)
[1] 4.111111
> mean(y)
[1] 5.222222
> cor(x,y) # +...
> x=c(5,3,1,6,4,3,2,6,7)
> y=c(7,4,1,8,5,2,4,7,9)
> mean(x)
[1] 4.111111
> mean(y)
[1] 5.222222
> cor(x,y) # + indicates consistency, more power
[1] 0.943973
> t.test (x,y,paired=T) #sig because of + correlation
Paired t-test
data: x and y
t = -3.1623, df = 8, p-value = 0.01335
alternative hypothesis: true difference in means is not equal to
0
95 percent confidence interval:
-1.9213584 -0.3008638
sample estimates:
mean of the differences
-1.111111
>
What conclusions can be made regarding statistical
significance?
Would...
Given the IVP x * sqrt(x+1) * y'''-y'+xy=0 when
y(1/2)=y'(1/2)=-1 , and y''(1/2)=1
determine the larest...
Given the IVP x * sqrt(x+1) * y'''-y'+xy=0 when
y(1/2)=y'(1/2)=-1 , and y''(1/2)=1
determine the larest interval for which the apporpriate
existsence and uniqueness therom gaurentees the exsistence of a
unique solution, show all work and fully justify why andhow you got
that interval.
(3)If H(x, y) = x^2 y^4 + x^4 y^2 + 3x^2 y^2 + 1, show that...
(3)If H(x, y) = x^2 y^4 + x^4 y^2 + 3x^2 y^2 + 1, show that H(x,
y) ≥ 0 for all (x, y). Hint: find the minimum value of H.
(4) Let f(x, y) = (y − x^2 ) (y − 2x^2 ). Show that the origin
is a critical point for f which is a saddle point, even though on
any line through the origin, f has a local minimum at (0, 0)
1. Show that the u1(x,y)=x and u2(x,y)=x^2-y^2 are solutions to
Laplace Equation.
Then, how can you...
1. Show that the u1(x,y)=x and u2(x,y)=x^2-y^2 are solutions to
Laplace Equation.
Then, how can you combine them to create new solutions.
Let X ~ N (1, 2^2) and Y ~ N (2, 2^2). Suppose that X and...
Let X ~ N (1, 2^2) and Y ~ N (2, 2^2). Suppose that X and Y are
independent. Let U = X + Y and V = X ̶Y. Show that U and V are
independent normal random variables. Find the distribution of each
of them.
MATHS CALCULUS
Find the coordinates of the point on the curve y^2 = (5/2)(x+1),
which is...
MATHS CALCULUS
Find the coordinates of the point on the curve y^2 = (5/2)(x+1),
which is nearest to the origin. I have minimised this using the
pythagorean distance formula, but the x value doesnt appear on the
curve and this has me confused.
A consumer has preferences represented by the utility function
u(x, y) = x^(1/2)*y^(1/2). (This means that...
A consumer has preferences represented by the utility function
u(x, y) = x^(1/2)*y^(1/2). (This means that
MUx=(1/2)x^(−1/2)*y^(1/2) and MUy =1/2x^(1/2)*y^(−1/2)
a. What is the marginal rate of substitution?
b. Suppose that the price of good x is 2, and the price of good
y is 1. The consumer’s income is 20. What is the optimal quantity
of x and y the consumer will choose?
c. Suppose the price of good x decreases to 1. The price of good
y and...