Express the bayes error rate in terms of the parameters

Assignment Help Advanced Statistics

Reference no: EM133341704

Problem 1: Suppose we have two random variables, X and Y, and we draw a sample from each as below. Use a Wilcoxon rank sum test to test the null hypothesis that X and Y follow the same distribution. Please report your results with interpretation.

X : 26, 30, 20, 21, 15, 34, 22

Y : 27, 23, 33, 29, 28, 18, 40, 12

Problem 2: Below is a 2x2 contingency table for two categorical variables X, Y. Perform Fisher's exact test to determine whether or not X and Y are independent. Be sure to include everything necessary to do the test, including a set of hypotheses, a significance level of your choice, and a fully-explained conclusion.

	Y = 0	Y = 1
X = 0	12	25
X = 1	3	7

Problem 3: Suppose that we have a classification problem with two classes, Y = 0 and Y = 1, and one feature measurement X . Suppose that

X|Y = 0 ∼ N(µ₀, σ₀²)
X|Y = 1 ∼ N(µ₁, σ₁²)

We will use 0-1 loss for this task. You may assume that a priori, both classes are equally likely.

1. Suppose that σ₀ = σ₁. Express the Bayes classifier in terms of the parameters. Express the Bayes error rate in terms of the parameters. You may leave your answer in the form of a sum of integrals for the Bayes error rate.

2. Suppose that µ₀ = µ₁, σ₀ ≠ σ₁. Express the Bayes classifier in terms of the param- eters. Express the Bayes error rate in terms of the parameters. You may leave your answer in the form of a sum of integrals for the Bayes error rate.

3. Suppose that µ₀ = µ₁, σ₀ = σ₁. Express the Bayes classifier in terms of the parameters. Express the Bayes error rate in terms of the parameters.

Reference no: EM133341704

Questions Cloud

Summarize overall health behaviors of family : Summarize the overall health behaviors of the family. Describe the current health of the family.

How much it will end up costing your company : Determined your (i) cost-minimizing level of capital and labor to meet the production requirements and (ii) how much it will end up costing your company.

Considering vulnerable populations : When considering vulnerable populations, many Americans are underinsured or uninsured

Explain how existence of adverse selection andmoral hazard : Using appropriate examples explain how the existence of adverse selection andmoral hazard in insurance markets can lead to market failure and under provision

Express the bayes error rate in terms of the parameters : Perform Fishers exact test to determine whether or not X and Y are independent. Be sure to include everything necessary to do the test

Why is the short-run average total cost curve u-shaped : How would advertising work in the model/world of perfect competition? Why is the short-run average total cost curve U-shaped?

Health plans participating in affordable care act : Health plans participating in the Affordable Care Act must be accredited; what is the difference between the National Committee for Quality Assurance

What about an amenity like accessible park-like waterfront : What about an amenity like an accessible park-like waterfront for a city? Richard Florida's theory of the creative class involves amenities like a city world

How this religion overcomes death and integrates self : Explain the key contributions this religion took from the work of Jacques Derrida. Explain the key contributions this religion took from the work of John Caputo

User Account

All Pages