0====Specificity or also referred to as True Negative RateP(T=0|D = 0)P(T=0nD = 0)P(D = 0)True Negatives1 - PrevalanceWe assume that X|(D0)~ Norm (50, 10) and X|(D = 1) ~ Norm(70, 15). In R there arefunctions 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 thehelp files to see the parameters of these functions. In this problem you are required to do the following1. 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*.= 5ProblemIn this problem we will plot the ROC curve for the example that we did class. We had defined the followingtwo random variablesn===D={T10=if sample is infectedif sample is not infectedThe 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{10test is positivetest is negativeSensitivity or also referred to as True Positive RateP(T=1|D = 1)P(T=1nD = 1)P(D = 1)True PositivesPrevalance

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

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...

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