Consider there are two populations one with attribute D = 1 and the other with attribute D = 0. A binary classifier with threshold a is used to categorize a given sample into one of the two populations. The classifier returns the result T = 1 if it determines the sample to be of type D = 1 otherwise it returns T = 0 and determines that the sample is of type D = 0. The random variable X measured by the classifier is distributed as follows: X|(D = 1) ~ Unif(10, 30) and X|(D = 0) ~ Unif(0, 20). 1. What is the Sensitivity (True Positive Rate)? 2. What is the Specificity (True Negative Rate)?

Consider there are two populations one with attribute D = 1 and the other with attribute D = 0. A binary classifier with threshold a is used to categorize a given sample into one of the two populations. The classifier returns the result T = 1 if it determines the sample to be of type D = 1 otherwise it returns T = 0 and determines that the sample is of type D = 0. The random variable X measured by the classifier is distributed as follows: X|(D = 1) ~ Unif(10, 30) and X|(D = 0) ~ Unif(0, 20). 1. What is the Sensitivity (True Positive Rate)? 2. What is the Specificity (True Negative Rate)?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

Let x be a random variable that represents hemoglobin count (HC) in grams per 100 milliliters of whole blood. Then x has a distribution that is approximately normal, with population mean of about 14 for healthy adult women. Suppose that a female patient has taken 10 laboratory blood tests during the past year. The HC data sent to the patient's doctor are as follows. 14 18 15 19 13 11 15 18 15 12 (i) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.) X = S = (ii) Does this information indicate that the population average HC for this patient is higher than 14? Use a = 0.01. (a) What is the level of significance? State the null and alternate hypotheses. О Но: и 3D 14;B Hі: и 14; Hі: и %3D 14 Но: и 14 О Но: и 3D 14;B Hi: и # 14 (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The standard normal, since we assume that x has a normal distribution and o is…
b. Let X1, X2, X3, and X4 represent the weight of shipment packages at a certain shipment facility. Suppose they are independent normal random variables with means H1 = 3.6, 42=0.9, 3= 1.8, 4 = 7.4 pounds and variances o = = = Find P (2X₁ + 1X2 + 3X3 + 1X4 ≤ 17.6). = 1.
Let a be a random variable representing the percentage of protein content for early bloom alfalfa hay. The average percentage protein content of such early bloom alfalfa should be u = 17.2%. A farmer's co-op is thinking of buying a large amount of baled hay but suspects that the hay is from a later summer cutting with lower protein content. A small amount of hay was removed from each bale of a random sample of 50 bales. The average protein content from the samples was determined by a local agricultural college to be -15.8% with a sample standard deviation of S = 5.3%- At a = .05, does this hay have lower average protein content than the early bloom alfalfa?
Given n independent policyholders with individual loss random variables X1, X2, ., Xn, such that the expected value of any policyholder's loss is pph and the variance is o. If the insurer is providing these n policyholders with insurance, find the following (the detailed steps are required): 1. The expected value of the insurer's average loss per policy; 2. The variance of the average loss per policy.
Let X1 and X2 be independent standard normal random variables. Show that the joint distribution of Y, = a11X1+A12X2 + b1 Y2 = a2] X1 + A22X2+ b2 %3D is bivariate normal.