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5 Problem In this problem we will plot the ROC curve for the example that we did class. We had defined the following two random variables ๆ = D = = { T 1 0 = if sample is infected if sample is not infected { 1 The ROC curve plots the True Positive Rate (which (which is also 1-0 where theta is the specificity). Recall that 0 test is positive test is negative is also the sensitivity n) against the False Positive Rate Sensitivity or also referred to as True Positive Rate P(T = 1|D = 1) D(T 100

5 Problem In this problem we will plot the ROC curve for the example that we did class. We had defined the following two random variables ๆ = D = = { T 1 0 = if sample is infected if sample is not infected { 1 The ROC curve plots the True Positive Rate (which (which is also 1-0 where theta is the specificity). Recall that 0 test is positive test is negative is also the sensitivity n) against the False Positive Rate Sensitivity or also referred to as True Positive Rate P(T = 1|D = 1) D(T 100

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.3: Measures Of Spread
Problem 1GP
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0 = = = = Specificity or also referred to as True Negative Rate P(T=0|D = 0) P(T=0nD = 0) P(D = 0) True Negatives 1 - Prevalance We assume that X|(D 0)~ Norm (50, 10) and X|(D = 1) ~ Norm(70, 15). In R there are functions to obtain both the probability density function (pdf) and the cumulative distribution function (cdf) of a random variable that has a Normal distribution. These functions are dnorm and pnorm. Review the help files to see the parameters of these functions. In this problem you are required to do the following 1. Plot the pdf and the cdf of X|(D = 1) ~ Norm(70, 15) for values 20 to 120. 2. Let x* denote the cutoff value such that if X > x* then the test is positive test otherwise it is consid- ered be negative. Plot the ROC curve for values of z* ranging from 52 < x ≤ 65. 3. If False Positive Rate and False Negative Rates are equally bad, determine the value of r*. =
Transcribed Image Text:0 = = = = Specificity or also referred to as True Negative Rate P(T=0|D = 0) P(T=0nD = 0) P(D = 0) True Negatives 1 - Prevalance We assume that X|(D 0)~ Norm (50, 10) and X|(D = 1) ~ Norm(70, 15). In R there are functions to obtain both the probability density function (pdf) and the cumulative distribution function (cdf) of a random variable that has a Normal distribution. These functions are dnorm and pnorm. Review the help files to see the parameters of these functions. In this problem you are required to do the following 1. Plot the pdf and the cdf of X|(D = 1) ~ Norm(70, 15) for values 20 to 120. 2. Let x* denote the cutoff value such that if X > x* then the test is positive test otherwise it is consid- ered be negative. Plot the ROC curve for values of z* ranging from 52 < x ≤ 65. 3. If False Positive Rate and False Negative Rates are equally bad, determine the value of r*. =
5 Problem In this problem we will plot the ROC curve for the example that we did class. We had defined the following two random variables n = = = D = { T 1 0 = if sample is infected if sample is not infected The ROC curve plots the True Positive Rate (which is also the sensitivity n) against the False Positive Rate (which is also 1 - 0 where theta is the specificity). Recall that { 1 0 test is positive test is negative Sensitivity or also referred to as True Positive Rate P(T=1|D = 1) P(T=1nD = 1) P(D = 1) True Positives Prevalance
Transcribed Image Text:5 Problem In this problem we will plot the ROC curve for the example that we did class. We had defined the following two random variables n = = = D = { T 1 0 = if sample is infected if sample is not infected The ROC curve plots the True Positive Rate (which is also the sensitivity n) against the False Positive Rate (which is also 1 - 0 where theta is the specificity). Recall that { 1 0 test is positive test is negative Sensitivity or also referred to as True Positive Rate P(T=1|D = 1) P(T=1nD = 1) P(D = 1) True Positives Prevalance
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          The ROC curve plots the True Positive Rate (which is also the sensitivity ŋ) against the False Positive Rate.

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