Problem 4. Consider two normal distributions with arbitrary but equal covariances. Prove that the Fisher linear...

Problem 4. Consider two normal distributions with arbitrary but equal covariances. Prove that the Fisher linear discriminant, for suitable threshold, can be derived from the negative of the log-likelihood ratio.

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orchestra answered 1 year ago

Linear Optimization (Math 423) Problem, prove an analog of the follow theorem: Thm 2.4: Consider the...

Linear Optimization (Math 423) Problem, prove an analog of the follow theorem: Thm 2.4: Consider the constraints Ax = b and x ≥ 0 and assume that the m X n matrix A has linearly independent rows. A vector x ∈ Rn is a basic solution if and only if we have Ax = b, and there exist indices B(1), ... , B(m) such that: (a} The columns AB(1),...,AB(m) are linearly independent; (b} If i ≠ B(1),...,B(m), then xi =...

Prove that if n is greater than or equal to 4 then the center of the...

Prove that if n is greater than or equal to 4 then the center of the alternating subgroup An is the trivial subgroup. What is Z(An) for n = 0,1,2,3 ?

What are two examples for normal distributions with numbers and formula?

4. Consider the linear program in problem 3. The value of the optimal solution is 48....

4. Consider the linear program in problem 3. The value of the optimal solution is 48. Suppose the right-hand side for constraint 1 is increased from 9 to 10. (problem 3 linear program) Min 8X+12Y s.t. 1X+3Y≥9 2X+2Y≥10 6X+2Y≥18 A,B≥0 A) Use the graphical solution procedure to find the new optimal solution. b) Use the solution to part (a) to determine the shadow price for constraint 1. c) The sensitivity report for the linear program in Problem 3 provides the...

prove that where a,b,c,d,e are real numbers with (a) not equal to zero. if this linear...

prove that where a,b,c,d,e are real numbers with (a) not equal to zero. if this linear equation ax+by=c has the same solution set as this one : ax+dy=e, then they are the same equation.

Consider the following data for two independent random samples taken from two normal populations with equal...

Consider the following data for two independent random samples taken from two normal populations with equal variances. Find the 95% confidence interval for µ1 - µ2. Sample 1: 11,5,12,9,6,8 Sample 2: 12,9,16,13,11,11 What are the left adn right endpoints?

In this problem we want to calculate the electric field due to several charge linear distributions...

In this problem we want to calculate the electric field due to several charge linear distributions .a) Consider a thin rod of length L. The rod carries a uniform charge density, λ, and total charge Q. Calculate the electric field at a point p that is on the rod’s cylindrical axis of symmetry and a distance d away from the end of the rod. Do this by direct integration. How does your expression be have as L→∞?b) Repeat, with the...

The assumptions of simple linear regression include: a) Equal variance of the error terms b) Normal...

The assumptions of simple linear regression include: a) Equal variance of the error terms b) Normal distribution of the error terms c) Independent study subjects d) Linear relationship between X and Y e) All of the above f) All except option c) Which of the following would not be a null hypothesis when performing a chi-square test? a) The populations are homogeneous. b) The row and column variables are independent. c) The row and column variables are related. d) The...

4. Given a linear programming optimization problem, with the choice of two products, we know in...

4. Given a linear programming optimization problem, with the choice of two products, we know in advance that a possible answer is to make only one product. 5. Cost minimization problems typically involve constraints which have the phrase “at least”. Please explain each answer in your own words 1. Please show what slack resources are graphically. You can draw a picture and scan it or take a picture and add it to the document. 2. Please given an example of...

4. For this problem, you’ll compare the hypergeometric and binomial distributions. Suppose there is a sock...

4. For this problem, you’ll compare the hypergeometric and binomial distributions. Suppose there is a sock drawer with N socks, each placed loosely in the drawer (not rolled into pairs). The total number of black socks is m. You take out a random sample of n < m socks. Assume all the socks are the same shape, size, etc. and that each sock is equally likely to be chosen. (a) Suppose the sampling is done without replacement. Calculate the probability...

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