Math Answers

Given the population 3, 5, 8, 9, and 10. Suppose samples of size 4 are drawn from this

population.

1. What is the mean (μ) and standard deviation (σ) of the population?

2. How many different samples of size n = 4 can be drawn from the population? List them with their corresponding means.

Sample Mean

1.

2.

3.

4.

5.

3. Construct the sampling distribution of the sample means.

Sample Mean𝐗̅ Frequency Probability(𝐗̅)

1.

2.

3.

4.

5.

6.

4. What is the mean (μX̅) of the sampling distribution of the sample means? Compare this to the mean of the population.

5. What is the standard deviation (σX̅) of the sampling distribution of the sample means? Compare this to the standard deviation of the population.

solve px+qy=y

What is the Jacobian matrix J(r, θ) for the polar coordinate transformation, given that x=rcos⁡θ and y=rsin⁡θ.

Select one:

A. cos⁡θ-rsin⁡θ-sin⁡θrcos⁡θ

B. -rcos⁡θsin⁡θsin⁡θ-rcos⁡θ

C. cos⁡θ-rsin⁡θsin⁡θ-rcos⁡θ

D. cos⁡θrsin⁡θsin⁡θrcos⁡θ

Evaluate limz→2i⁡(iz^4+3z^2-10i)

Select one:

A. -12-6i

B. 12+6i

C. 12-6i

D. -12+6i

Evaluate ∇2U, given that Ux,y,z=xy2z3

Select one:

A. y2z3+2xz3+6xy2z

B. x2y2z+2xz3-6xy2z

C. y2z3+2xyz3+3xy2z2

D. 2xz3+6xy2z

Find the vector joining the points P(2, 3, 0) and Q(-1, -2, -4) directed from P to Q.

Select one:

A. 3i-5j-4k

B. 3i-5j+4k

C. 3i+5j-4k

D. -3i-5j-4k

Compute the divergence of the vector field exy2i+x+2yj

Select one:

A. exy2+2

B. y2+2

C. 2exy

D. exy2+2x+y

1. Samples of eight cards are drawn at random from a population of nine cards numbered from 1 to 9.

a. How many possible samples can be drawn?

b. Construct the sampling distribution of sample means.

Let Q(x, y) denote the statement “x is the capital of y.”

What are these truth values?

a) Q(Denver, Colorado)

b) Q(Detroit, Michigan)

c) Q(Massachusetts, Boston)

d) Q(New York, New York)